I'm torn with this. She is your bunny, you clearly love her and are doing your best for her. I have 4 indoor buns, have had all my buns inside with me since I was 15 so I could spend more time with them. I agree with what others have said that if she goes outdoors with your nan or someone else who is not too bothered with her, she is definitely better off indoors with you. What's so great about being outside anyway? It's cold, wet, windy in winter (and summer here!) and on rare occasions, boiling hot. Then you have the risk of predators getting at her outside and frightening her to death even if they can't physically get at her. So I agree that she is much better off with you and they should hand her over to you as you are an adult now and she is your bunny.
But I am not that much older than you - 23 - and also live in my own place, job etc, but I still toe the line with my dad and step mum as I am programmed to seek their approval. I'm just beginning to stand up for myself and go against their wishes if it's something I care about - like a pet for example - and they have surprised me by not making a fuss and going, "you're an adult now, we're always here for you, but we don't care what you do, it's your life". This was a conversation we had on Saturday and I tested them by showing them my tattoo and they never batted an eyelid (these are people who have previously said tattooed people make themselves unemployable). And they were quite sad that I admitted if they'd not said that first, I'd have never told them out of fear. Families are complicated, and its easy for us to sit here going "tell them where to stick it and insist she is returned to you" without knowing the back story and your family history.
All I will say is that I hope you can stand up for yourself and Lola as it would be such a shame if you lost her when you obviously love her, but I understand it could be tricky if there is something going on that we don't know about.
PS, my mum sold my rabbit behind my back when I was on holiday when I was 15 - her reasoning was we were moving into a flat (she was an indoor bunny anyway!! And my dad had already agreed to take her to his house so my step brothers and sister could look after her and I'd see her when I stayed with them. Everyone's happy. I just found out from my grandma on Sunday that she actually did it so they couldn't have her. "She was my rabbit and not going to those other children." Yeah, so she went to another family and I never saw her again.... ooooo I'm fuming just thinking of it
)