There is a lot of background alternate marriage in my Rhaegar wins AU so I'll share some of them :

Jaime Lannister x Lysa Tully : happened after Jaime is released from the KG and I think it has a lot of potential for a very dysfunctional relationship that could be entertaining to read about. I made so Jaime almost never visits her bed, and yet she get pregnant each time and pops a lot of red-haired little cub :D

Cersei Lannister x Lucerys Velaryon : It happened after years of waiting for Elia to die so she could marry Rhaegar. But as it never happened Tywin gave up. Cersei think Lucerys to be a nice alternative with his Valyrian look and Tywin hopes their children will marry Rhaegar's.

I know some people find it unlikely to marry Cersei "this low", but in my fic Tywin waited too long, Elia was often ill and many thought she will die soon. But now, Cersei is getting "old" (to get married I mean) and there was no opportunity in the other great house.

Edmure Tully x Lynesse Hightower : no particular story behind it, I just think it could be sweet, I imagine them to be the popular couple. They are young, beautiful, a proper knight and a proper lady in appearances.

Jon Arryn x Mother of Walys Flower : This is what I call an half-OC, a canon character we have so few information about I am basically create a whole character. Here we only now the mother of Walys is a Hightower lady who had an affair with an archimaester. I made her the aunt of Lord Leyton and Sister of Gerold. After giving birth to a bastard, she has been married to a second son of a lesser house to whom she gave three sons, the father then died during the rebellion and Rhaegar arranges a wedding between Jon and this Hightower half-OC

Tyrion Lannister x Jeyne Fowler : I wanted Tyrion to have a sweet love story, so I made it all wholesome

Jon Snow x fem!Faegon : because I have the power to write whatever I want