I bed share, don't see anything wrong with that. I did it with my first baby and now wih my second. My baby never wants me to put her down at night. If I did, I would never get sleep.
Your baby is going to sleep how she wants to. You can't force her to sleep on her back. My daughter has been sleeping on her belly since she was 3-4 weeks old. That's how she wants to sleep. Wouldn't sleep any other way. Her pediatrician said it was perfectly fine for her to sleep on her tummy.
Put a swimming pool noodle under the sheets, she won't be able to push it away