Why force her into that marriage, simple money, power, and peace. House Velaryron was very much at the height of their power during this time. They were the richest family in the 7 Kingdoms and they were also a great military power, their navy was the most powerful, take into consideration that the Sea Snake Corlys Velaryon was very close to Daemon Targaryen(prince and before Rhaenyra was named heir he was the presumed heir) he supported Daemon's conquest of the stepstones even married his daughter off to Daemon, he was also married to Rhaenys Targaryen who was passed over for the throne, and their son Laenor was also passed over for the iron throne.
House Velaryon could easily have posed a great threat to the iron throne, they had already been gathering forces during the time of Jaehaerys to "defend" Laenor claim to the throne, and the reason it did not go further was the great council was called to resolve the issue of who was to be Jaehaerys' heir. During that council they were supported by Starks and Baratheons as well as House Blackwood(major riverlands family militarily more powerful than the Tullys). Plus we can not forget they also had Dragonriders of their own.
Viserys wanted to keep the peace and prosperity of Jaehaerys going and a political marriage to unite arguably the two most powerful families in the 7 kingdoms seemed like a good idea. Yeah everyone did know Leanor was gay but his family and most other thought that being married to the heir to the iron throne would put a little starch in his pants for her. They were totally wrong of course.
The Dance of the Dragons was inevitable looking at the the scenarios someone was going to be pissed when Viserys died and was going to try to take the throne from whoever sat on it. Daemon had ambition to sit on it, Corlys wanted someone from his family to sit on it, Rhaenyra wanted to sit on it, ironically Aegon II apparently didnt want to be King and had to be talked into it. Too many factions vying for one throne Viserys was screwed no matter what he did during his reign.