I split up with my girlfriend 2 months ago. We have a 1 year old and she won't let me see her?

I have been seeing her every weekend by travelling 4 hours by car on Saturday, picking her up and taking her to a B&B in Devon where she lives and staying with her until Monday. Her mum has no contact with her in that time. This weekend that just ped, I decided to bring her back to London with me on the Saturday as she has SO MUCH extended family here who have not seen her for a while. She had SUCH a great weekend with her Granddad, Grandmother, Uncles, Aunties, cousins and friends and their kids. I didn't tell my ex that I was bringing her here because she would get nasty with me and try to stop me seeing her as she doesn't want her coming here. The reasons she gives have no basis in reality. She says that she will be too far away from the little one - our daughter is fine with me and I do everything for her better than most women can! Anyway, my ex was away this weekend so she wasn't near her regardless! She also says that it's too far for a 1 year old to travel in a car in the rear by herself - I stopped twice on the way back and fed her and changed her and she was absolutely fine. She slept much of the way anyway, and slept ALL of the way TO London. I have even suggested bringing someone with me everytime I want to bring her back so that they can sit in the back with her but she simply does not want her to come here. My suspicions are that her reasons are more about being nasty, mean and controlling. She is not thinking of what is best for our daughter as that is clearly for her to have contact with her family. Will a court forbid me from bringing her here to London to her family? I umed that what I do with her on my time is my business as long as I take good care of her??! What can I do as she insists that we go through solicitors now?