OP, apply for the court order today - presumably based on the existing sharing arrangements but specifying that a qualified childcare professional/relative/other nominated adult can collect from his house/be at yours at dropoff on your days.
Then at the same time, book a mediation session to specify the same thing. You can find your nearest using this https://www.gov.uk/looking-after-children-divorce/mediation
If he refuses to attend mediation, that will go in your favour when it reaches court.
What is he going to try to argue - that you shouldn't be working to pay for childcare? He has 2 options here: look after his own children an extra night short term; or let them leave with your nominated childcare professional.
He can't cast you as a poor parent for furthering your career for the sake of 4 hours childcare a week - that's just not going to land with the court.
So accept the job, or you'll be arguing about a hypothetical situation anyway.
Unless there's some MASSIVE drip feed that your children are 20 months & 4 month old twins, or 1,3&5 with SEN, you need to just get on with accepting the job & making it work!
I'm sure it's daunting & good luck, but you can do it! 