Han Solo accepts Isolder's Offer of the Nova-Class Battle Cruiser.

How does this decision affect the later events in the Legends verse. (Leia marries Isolder instead of Han).

Additionally, what does Han do with his new ship?

 

If he accepted the offer, Han must have flown far away and never come back. That was the deal, right?

Honestly, I can't see him accepting that at all, totally not in his personality. Isolder wouldn't have wasted his time making the offer if he understood Han.

 

How does this even make sense? Han would never give Leia up without a fight, and he would rather die than give up the Falcon.

 

Getting the warship doesn't mean Han gives up the Falcon. This is just a what-if scenario -- although it is one that almost certainly would never have happened for the reasons stated by @Sarge.

Also, nobody answered the question of how the marriage affects the universe as a whole.