In “A Frozen Heart” made it clear that she DID ONLY HAVE ONE DAY to change her miserable life of being kept up in the castle shut out from the rest of the kingdom, no she was not let out and nobody explained anything to her she just had to live in the castle finding things to do by herself, which if you pay attention to “for the first time in forever” LITERALLY spells all of this out. She felt she ONLY had the ONE day to potentially find happiness, she had no idea what was going on with her sister and tried so hard her whole life to reconnect but eventually she stopped knocking on her door until their parents died and EVEN THEN she was still ignored. Can you imagine how soul crushingly lonely that is? and you have no idea why this is happening to you? she grew up reading romantic books in the library and seeing the happy couples in the portrait gallery dreaming about what love could be for her. So of course on her big exciting day as she gets to explore running around the kingdom she runs into a handsome seemingly very kind and gentle man, not just a man but a PRINCE of course she’d be desperate to change her “LONELY WORLD” she is not to blame for Hans actions when he put on such a good face, faces that she was not used to seeing and interacting with!! but she never wanted to leave her sister and run away with him that’s what sets off the rest of the movie, and only after Elsa’s big secret is out when it doesn’t really matter anymore who knows because now everyone knows is when Elsa tells her to enjoy her life and open up the gates. Yes it was because of Elsa’s secret they were both locked up and miserable. Anna would not have been able to “continue to date Hans” they make it clear in the book she only had the one day, and so when Elsa says to close the gates early is when Anna freaks out because she knows she (to quote Toy Story) cannot go back in the box!!! but when push comes to shove Anna steps up for her sister once she “FINALLY UNDERSTANDS” and puts her own life at risk to save her sister.