My daughter is 3 (almost 4) and we've been living with my BF full time for about 3 months (we slowly transitioned, starting by only staying at his house 2 days a week and then gradually increased that to full time for the past 3 months). In the beginning it was great. Everyone got along, my daughter loved my BF. She eventually would tell him "bye, I love you too" every time we left the house. Then, about 6 weeks ago that started to change. She wouldn't say I love you and then she started saying "I don't love you" or "I only love you outside the house", etc...We also took her out of daycare at this point, so a lot of changes are going on and I know this is normal. I know she feels threatened by my BF taking time away from her, etc...
But now it's getting even worse. She is telling me he is hitting her. She says he's a bad man and he's bad to her. Last night at dinner she said he hit her across the room and kicked her in the chest. When I asked her when he did this she said, "Now." I asked her if she was lying and she said no, but I asked her if she knew what a lie was and she also said no (another time we talked about lying she told me later in the day that her imaginary mouse friend died because he lied, so I am pretty sure she doesn't totally understand the concept). I tried to explain what lying was at that point and she then told me my BFs daughter hit her with a pillow (probably true). But then she went back to saying my BF hit her.
Now, I realize my judgment could be clouded and I need to be careful that he's not actually hitting her, but there have been no marks or bruises, he's never hit anyone (not me or his kids), he hates hitting, he's very open about everything (I have access to his electronic devices, passwords, etc) so I doubt he's hiding some secret double life. But of course I am still slightly concerned. But 90% of the time he is alone with her I am somewhere in the house (working so behind a locked door).
So is this normal? How long should I expect it to last? There are lots of times where she enjoys being with him. I can hear them laughing together, she wants to make him cards and show him things she's made, they read together, play games, etc...she always wants to go to the store with him.
My other question is how do I teach her that lying about someone hitting her is wrong, but still let her know it is important for her to tell me if someone is really hurting her and that I will protect her?
None of what you described sounds too unusual to me. She's too young to get lying and all of the implications of accusing a grown man of hitting her. It sounds like most of this is her three year old way of dealing with her more negative feelings about all the changes. I wouldn't be surprised if this is totally a thing of the past within six months.
Getting through to her about the consequences of lying, maybe you could tell her the story of the boy who cried wolf (my kids learned a lot of stuff through stories when they were little, maybe that would work with yours?). Let her know that if her body is hurt, you want to know right away so you can help her and keep her from getting hurt again. And then say that if she is angry at someone, even someone both of you love, that you want to listen to her tell how she feels. Maybe she'll stop the accusations if she knows there's a more direct route for her to express herself, and that you will accept her feelings when she shares them.