I do understand all the posters saying to @mummy917 not to arrange Friday childcare.
I was assuming that the nursery would not accept an every-other-Friday booking, so it would be all Fridays or none. Which means if OP did need to work Thursday nights for the money, it would have to mean paying for nursery every Friday.
The suggestion that OP asks his mother to pay half has two purposes: one to actually help financially, and two to signal to her that her son is a complete dickhead who is ducking out of his responsibilities. That would trigger the difficult "conversation" between her and her son, which would move the situation along nicely.
Another consideration is the long term future - if nursery places are like gold dust in that area, it may be a case of seizing the slot as soon as it is available. Assuming the 50/50 falls apart and OP gets an agreement for more nights in court, more childcare will need to be lined up and ready. The mediation-plus-court process will be in about November or December, which is only a few months away.
Of course in theory dickhead should pay his half, and OP should not bail him out. But the reality is that he won't actually pay his half - it will need to be deducted from his share of the financial settlement, if his mother does not pay.
However @mummy917 , your alternative of simply not working nights every other Thursday is also a valid strategy - you will present evidence to the court of his refusal to facilitate you earning, therefore you need more maintenance from him and/or a bigger share of the assets when they are split.
(Don't forget that court-ordered maintenance is a separate thing from CMS calculated maintenance, though I believe CMS can be used to enforce a court order; check with your solicitor at the time)
To use a metaphor, this is not a boxing match. It is not about scoring points now. It is a combination of chess and poker: what is needed is strategic long-term thinking with a blank face that gives away no clues.