It would appear you ex has acted entirely within the rules for claiming funded childcare. He has evidently been able to register with the government website and obtain the 30 hours code number.
I’ve seen various local authority claim forms and user agreements: all those I’ve seen require only one parent to provide details and instruct the childcare provider. The general principle is that the funding 'belongs' to the child, and assumes the parents will jointly and severally make responsible decisions on the child’s behalf as to how it is used. The system does not make provision for resolving disputes between parents.
Please remember also, the childminder is providing a childcare/education service, and she is not responsible for resolving your interpersonal conflicts either. Her first duty is towards the child, not to take sides between parents. She is legally required to treat both parents equally and respect their individual rights and interests. This may seem obvious, and I’m not suggesting you’d take advantage. But it is extremely common for warring parents to try to get the childminder on their side; IME this almost always involves the mum's side.
It appears your ex now has a formal arrangement in place with the childminder.
The three of you need to sit down together and make whatever adjustments you can all agree. In a sense, you don’t have to go along with what your ex has arranged. You don’t have to take the child at the arranged times, and you’re within your rights to collect any time.
But this approach is almost certain to have consequences. In my area, a childminder is required to obtain evidence of absences and report poor attendance within afunding arrangement for investigation by the Children’s Social Care Services. The funding department would refuse to pay for the absences, so the childminder is likely to charge them back to you. She has a general responsibility to ensure funded places (which are in short supply) are used properly, so there’s some chance you’d lose the funded place. You can’t rule out losing the childcare place altogether, if the whole thing becomes too disruptive for the childminder and/or other families. Again, parents in conflict are frequently blind to the impact they’re having on people around them, so do have a thought and proceed with caution.