One More Wife
To complicate the issue yet a little bit further, if we take Plato's dialogue Kritias into account, Poseidon actually has three wives, not just two. According to the description of the foundation of Atlantis in Kritias, Poseidon was married to a certain Kleïto [Cleïto] who bore him five sets of twin sons who ruled the land, which was named Atlantis after the eldest of these brothers, called Atlas.
There may, however, be a way to look at it so that, in spite of the extremely high profile wedding unions assigned to Poseidon with each of these three figures, he is not necessarily polygamous. Indeed Ancient Greek culture, despite the philandering, was typically monogamous, as were its deities, these entities being an enhanced projection of said culture.
Kleïto is perhaps the least problematic wrinkle herein, since it is relatively easy to solve her involvement with Poseidon chronologically: she was simply his primordial wife, before he had met Amphitrite. Kleïto appears to have been mortal (both her parents are described simply as Autokhthones [Autochthons], "Earth-Sprung" people), and her death (likely in old age), as well as the cataclysmic destruction of Atlantis, are probably supposed to have occurred long before Poseidon's [second] wedding.
Amphitrite in Other Literature
The story of Beroe's marriage to Poseidon appears in no other place apart from Nonnus' epic Dionysiaka, which on many points quite evidently seeks to imitate certain styles and tropes of the much older epic of Homer's Iliad. A feature shared by Kritias, the Dionysiaka and the Iliad is that Amphitrite fails to appear in any of them.
Out of thirty-three Nereids named in the Iliad, Amphitrite is not one of them, which is quite surprising considering Poseidon's prominence in the poem on the one hand while, on the other hand, there is the fact that obscure but similarly-named Nereids like Amphinome and Amphithoe are granted their own Iliad cameos.
Amphitrite is mentioned very few times in Homer's Odyssey, indeed as a major sea-goddess but never as Poseidon's wife. Neither the Iliad nor the Odyssey say anything about the more famous offspring of Poseidon and Amphitrite, namely the merman Triton and the sea-nymph Rhode. Homer simply does not seem to know of such a relationship between this Nereid and the Sea-King.
We do know, though, that as early as Hesiod's Theogony, which is supposed to be contemporaneous with Homer, Amphitrite is in fact known to have been married to Poseidon and borne him the afore-named children. While Nonnus never mentions Amphitrite, Triton does appear a few times in the Dionysiaka. In every source which mentions his parentage, he is always the son of Poseidon and Amphitrite. Presumably we are to understand him the same way here although Nonnus does not explicitly provide us with any familial link between the merman sea-god and anyone else.
There are perhaps three different ways of interpreting this. One is that Amphitrite does exist in the Dionysiaka (somewhere so far in the background that she receives zero airtime), has borne Triton to Poseidon at some point, but was never married to him. So when Poseidon first encounters Beroe, he is a (somewhat) eligible bachelor.
Nuptial Terminology in the Dionysiaka
A second interpretation would recognise the manner in which language about marriage is used by Nonnus, for whom it is almost standard that a sexual encounter equals some sort of conjugal union, no matter how brief the interaction between the partners. Nor in fact does it seem to matter in several cases that the encounter is not consensual. Most of the time that Nonnus mentions a bride or a bridegroom, there is obviously no wedding ceremony that has been officiated nor would anyone understand the couple in question to be legally married on any level beyond the bodily consummation having transpired.
Often in the Dionysiaka even the act of abduction before this consummation is a "wedding," such as when Zeus takes Europa to Crete (3.323-324) or transforms into an eagle to kidnap the Naiad Aigina [Aegina] (8.247). Him carrying these women off makes each of them into his bride (nýmphe). Similar “bridal” terminology occurs in Book 13 when Apollon [Apollo] steals the Naiad Kyrene [Cyrene] away to Libya. In Book 8, Hera, having learned of the secret affair between Zeus and Dionysos' [Dionysus'] mother Semele, in a speech to Semele herself, says that the Theban princess is claiming Zeus as her bridegroom (nymphíos).
Incidentally, during the competition between Poseidon and Dionysos for Beroe, a similar affair between the Sea-King and a different woman is referred to, by Dionysos himself, as a wedding. This is in Book 42, when Dionysos is telling Beroe that Poseidon once disguised himself as the river-god Enipeus in order to have his way with the Thessalian princess Tyro, who was in love with Enipeus.
After Dionysos loses Beroe to Poseidon, Eros consoles him by telling him about a different prospect elsewhere, namely the Phrygian huntress Aura, whom Dionysos encounters in the 48th and last book of the epic. This book begins with Dionysos going to a lot of trouble in order to marry the Thracian princess Pallene, whom he seems to promptly forget about shortly after the wedding.
The second half of the book is taken up with the sordid and grisly misadventure which Aura goes through when she gets raped in her sleep by Dionysos and gives birth especially painfully to his twin sons, one of whom she kills violently before being turned into a spring by Zeus.
All within this same book, four different characters are named as "brides" of Dionysos: Ariadne, whom he lost in his battle against his half-brother Perseus (in the previous book); Pallene, to whom he clearly seems to be legally wed; Nikaia [Nicaea], another Phrygian whom he had also raped in her sleep back in Book 16; and Aura, who, upon discovering her pregnancy, refers to herself as the god's bride, albeit in very negative terms, e.g. dysgamē, "ill-wedded."
With Pallene most likely being mortal, it's possible that enough time has passed for her to grow old and die before Dionysos leaves Thrace to go find Aura in Phrygia. From this perspective, at any rate, marriage does not seem to be taken as seriously as one might otherwise expect, or its conventions are at least different.
Nikaia is clearly still alive in Book 48, and, being from the same geographical region, she even helps Aura to give birth specifically because they are both victims of Dionysos forcing himself upon them. Towards the conclusion of all this Dionysos is "triumphant and proud of his two Phrygian marriages, with the elder wife and the younger bride", i.e. Nikaia and Aura respectively.
With that, it is more plausible for Poseidon to actually be married to Amphitrite and Beroe at the same time. As loosely-held as that might make marriages here, however, it would in fact make Poseidon polygamous; and as with Dionysos and Pallene, the scene at the end of the contest between Poseidon and Dionysos does seem to be a full-on wedding.
Breaking Things Off
There might yet be one more option. Divorce among the gods is not unheard-of. Zeus is the prime example in Hesiod's Theogony, where he gets married six separate times before (sort of) settling down with Hera. In the Dionysiaka, Phaethon, the son of Helios and Klymene [Clymene], grows up with his parents in apparently the same home. In earlier works, however (e.g. Ovid's Metamorphoses and Euripides' Phaethon), it appears that Klymene, who at one point is wed to Helios, later leaves him for King Merops of Aithiopia [Ethiopia], in whose court Phaethon grows up, perhaps never having met his biological father before growing up.
As for Helios, he, on some later occasion, is betrothed to Rhode, who is usually a daughter of Poseidon and Amphitrite. But Asclepiades, in an one obscure source, says that Helios was her father, and presumably in that case she was not married to the Sun. It is not out of the question that Amphitrite had an affair with Helios, thus bearing him a child, but, as with previous examples, perhaps Asclepiades preserves here a tradition in which Helios was married to Amphitrite after she got a divorce from Poseidon.
Almost all of the characters to whom Helios is ever said to have been married are Oceanids, and, as you note in your Question, Amphitrite is an Oceanid in at least one source. At any rate we do not require such a connection between Helios and Amphitrite in order for this sea-goddess to be divorced from Poseidon. Her marriage to the Sea-King could simply be over by the time that he is granted Beroe in Dionysiaka 43.