If when your daughter reaches an appropriate age, her mother is still objecting then you'll need to book (and probably pay for unless you're on a low income) mediation on the matter, before any legal route can be taken. A
C100 application specifically asks for evidence of mediation, or a justification of why there hasn't been any. So, arrange
mediation. It may well achieve the desired aim, but if it unfortunately fails, you'll then be in the correct position to take the matter further (ie. to court)
I've been through the family court, I picked up a few useful skills and tips during that time. If you need help or support (I wouldn't say advice as I'm not a lawyer) feel free to PM.