You forget that everything of Rhaegar trumps Lyanna.
Man>Woman
Adult>Child
Prince>Lady
She could have realized that as the crown prince, he could have fucked her life and her family's is she didn't do as he asked. Also, we have no context of Rhaegar loving Lyanna, some people said it but it could have been something of denial since they desperately wanted to believe that Rhaegar was a good man and not mad like his father. However, I don't believe it was a kidnapping, I believe Rhaegar was obsessed with his predictions and realized that Elia could not have more children, so he needed a spare woman(the dragon has three heads). So seeing that Visenya was a warrior with pride, he needed someone like her, and since Lyanna was a wolf, she was perfect. So Rhaegar seduced her, and when he thought it was time, he got her to come with him. So I believe that Rhaegar did not love her, he only saw a an innocent girl he could convince to give him what he wanted. Rhaegar wasn't evil however, just blind sighted by his goals and fables.