As someone has already commented, the confusion is between Aegeus and Poseidon. This question does not have many alternate interpretations, it's just that it's never made clear, who the father of Theseus is. In Wikipedia the double paternity is addressed:
Still without a male heir, Aegeus asked the oracle at Delphi for advice. Her cryptic words were "Do ...
The string or thread is certainly well supported in Greek and Roman sources. (Emphasis mine, in all cases)
When he arrived at Crete, as most of the ancient historians as well as poets tell us, having a clue of thread given him by Ariadne, who had fallen in love with him, and being instructed by her how to use it so as to conduct him ...
Apollodorus' Epitome 1.24:
Theseus, arriving in the realm of Haides [Hades] with Peirithous
[Pirithous], was thoroughly deceived, for Haides on the pretense of
hospitality had them sit first upon the throne of Lethe. Their bodies
grew onto it, and were held down by the serpent's coils. Now
Peirithous remained fast there for all time, but ...
He was exiled from Athens and ended up on Skyros [Scyros] Island where he died falling off a high cliff, apparently murdered. His adventures sort of continue, to some extent, long after his death.
Going back in time to when Theseus’ father Aigeus [Aegeus] was still alive, Apollodorus tells us of a version of the story in which Aigeus’ father is not Pandion, ...
The Wikipedia article for Theseus ends its introduction with this:
As the subject of myth, the existence of Theseus as a real person has
not been proven, but scholars believe that he may have been alive
during the Late Bronze Age possibly as a king in the 8th or 9th
This assertion is based on Classical Mythology Tenth Edition. Quoting ...
The oldest written accounts are ambiguous on this point, so it is somewhat difficult to ascertain whether these two are not, in fact, merely aspects of the same tradition rather than two completely distinct, contradictory ones.
Hesiod, in his Theogony (c. 700 BC), simply says that Dionysus married Ariadne, with no mention at all of Theseus. The one source ...
Well it depends which source you want to follow.
If it is Plutarch, then he is dead.
Now in Euripides' tragedy "Herakles", the hero frees Theseus from the Hades From what I recall, the events are in Thebes, where Lycus usurped the throne and acted as a tyrant. Herakles' wife is there and Lycus is trying to kill her and her sons but as Herakles is in Hell ...
According to Theoi, Plutarch was taking legends and myths and trying to approach them historically.
Romulus (along with his twin brother Remus) was one of the legendary founders of Rome, and his mythological origin was that he was born to a Vestal virgin who was raped by the war-god Mars:
As Silvia one day went into the sacred grove, to draw water for ...
According to Diodorus Siculus, it was Herakles favour of Theseus that persuaded Hades to release him:
Peirithoos now decided to seek the hand of Persephone in marriage, and when he asked Theseus to make the journey with him Theseus at first endeavoured to dissuade him and to turn him away from such a deed as being impious; but since Peirithoos firmly ...
I have read in a book (I forgot the name but it had to do with the 12 tasks Herakles had to do) and it said that in one task Herakles ran across Theseus, as stated in your question, and when asking Hades to get Cerberus, he asked if Hades could free Theseus and Hades agreed. Theseus and Herakles then lived a normal life.
This is a follow-up to the accepted answer, which I think provides a good account for Pittheus' motivation, as backed up by the entry for Pittheus in The Oxford Classical Dictionary (4th edn):
[Pittheus] got [Aegeus] drunk and put him to bed with his daughter Aethra, thus becoming the grandfather of Theseus and creating a family tie between his own small ...
Since his purpose was to get him to sleep with his daughter, he must have deduced that the resulting son would be something special, and special enough to risk angering Aegeus.
At least, on the face of it. There are no myths that go into what he was thinking.
Four years, according to the introductory plot summary of Seneca's play Phaedra, is the amount of time Theseus was in the Underworld.
The Mechanics Thereof
I think you've answered your own concern regarding how it is Theseus and Peirithous were able to remain alive while they were trapped in the Underworld. Considering the powers possessed by the gods and ...
There are two textual sources for this, there is no mention for Dionysos' motivation:
Pausanias, Description of Greece, Chapter 20:
The oldest sanctuary of Dionysus is near the theater. Within the
precincts are two temples and two statues of Dionysus, the Eleuthereus
（Deliverer） and the one Alcamenes made of ivory and gold. There are
paintings here—Dionysus ...