If he can have the children full time and get a childminder to cover his shifts, great! Good for him!
You are able and willing to provide a minimum of 50% of the child care on a weekly basis. Plus you agree it's in the best interest of the children both of you remain active in their lives.
Therefore he can extend his logical solution. He puts that in place, he (or childminder) then has the children 50% of the time on a regular schedule and you have them the other 50%.
So that threat is a stupid one to try argue in court.
The court wont expect you to fund child care costs on "his days" and why would you pay him (his childminder) to look after your children when you are willing and able to do it on "your" days.
You are entitled to hold down a full time job to earn an living. Thats what the ex is doing. Having you earning reduces the risk that the children end up in a cycle of poverty, so again best interest of the children applies.
You have a right to have your own life too. He left, he cant expect the same relationship dynamic now that he is off living his life. If your prior relationship had evolved into a situation where he needs were met at the expense of your needs, you need to change your mindset. You need to put your life first. If his request has a negitive impact on your life and he benefits your starting point should always be a polite refusal with a suggestion that he (not you) comes up with some alternative arrangements. Dont be the first to offer a compromise or a solution to his problem.
Similar if you request something always try to offer alternatives so that the dynamic is a dialogue not a demand.
I suggest that if you are not already doing so you restrict your communication about care arrangements to some form of written communication.
First gives proof of who said what and a time line.
It also removes some of the emotional blackmail as you can restrict your communication to "action" verbs and dont include "feeling" verbs or respond to his emotional comments.
Sit down and work out a regular schedule that is fair and works for you and the children. Whats the week to week split, who picks up/drops off the DC.
Think about holidays and if you want them travelling out of the country.
Birthdays and any other special days. Whats possible eg can you both see the DC on each day or could it be moved to another day or swap each year.
Think about extra associated costs. Simple stuff, birthdays, if he has the child on that day, is there a party, who organises what, who pays, is DC sent to you for tea etc.
Have a read through other threads and get a feel for what issues you may wish to include in the aagreement.
You know his personality and how he is likely to react but always remember you are entitled to say no and let the court decide if you are being unreasonable.🌻