With regards to the negotiations Tywin had entered into to marry Jaime to Lysa Tully: “Lord Tywin … had gone so far as to invite Lord Hoster to the city to discuss dower.” – In these negotiations, which party would be negotiating from the strongest position (to what degree)? Would you agree with @JoannaLannister who thinks that Hoster had Tywin over a barrel? Thank You – RSAFan

Well, the fact that they’re talking about dower for Jaime vs. dowry for Lysa suggests that Hoster had the upper hand. I think @joannalannister makes some good points about Tywin not having much room to run in the non-Southron Ambitions camp because of his poor relationship with Aerys. Now, if Aerys died and Rhaegar became king, I think he could make a play to lead the new regime and a marriage alliance could help with that. 

The only thing that I would suggest differenty is that there must have been some eligible Tyrells, surely. 15+ years ago, was Janna married to Jon Fossoway or Mina to Paxter Redwyne, and there must have been an unmarried cousin.