girlfriend lives with her ex and his dad

so i started talking to this girl around august time and we got on great she mentioned her and her boyfriend had just went on a break when we started speaking but i didn’t really think much of it as i didn’t see her like that at the start, couple months go by and she fully cut things off with him and confessed that she liked me and by that point i had feelings as well so around mid October we started dating however this was when she told me she lived with her ex and his dad after she moved in to get away from her family and i was very sceptical at first until she reassured me that they now sleep in different rooms and don’t speak to each other that much, around november we had our first argument which was a silly one but could be resolved very quick as it was a small miscommunication however instead of doing that she got upset an ended up asking for some alone time only for me to find out she went on a late night drive with her ex that night, yes her ex is able to drive and i’m not as i’m not in the best place financially so lessons are not on the table right now but that first incident made her get very defensive when i brung it up, she started saying that she didn’t wanna not go on that drive etc.. anyway every time she wants to go shopping or go out to walk the dog she always goes with him an they drive around and hang out a lot and i asked her why doesn’t she go with me and her response was that she feels safer with him and that he drives so she will always be going out with him and i asked if that will be the case still months down the line and she said yeah so i felt weird about that, recently she has started to leave me delivered and sometimes on opened on our messages which makes me think she’s getting distant, i don’t know what to do like i love her but i also hate the fact she lives with her ex, is this something i should break off or trust the process