I don't think this sounds fair at all.
Your ex wants your child on his days off work when it suits him. So is he expecting no child care costs? and will get to spend 100% of his free time with the child.
OP on the other hand is supposed to try and find childcare on changing days or ask her workplace to have constant flexibility on her shifts or availability for meetings etc? Ok then!!
EX - Mo,Tu,We,th
OP - Fr,Sa,Su,Mo
Ex - tu,we,th,fr
OP - sa,su,mo,tu
Ex - we,th,fr,sa
OP su,mo,tu,we
Assuming the OP works full time Monday - Friday, she would potentially need childcare (I.e. before & after school or nursery) Week 1: Friday and week 2: Monday, week 3: Monday & Tuesday, week 4: Tuesday and Wednesday.
Who has ever heard of a nursery offering random days on a permanent basis?! My experience is that they will only accept fixed days, the same each week.
I guess the child could go to nursery on fixed days each week (which is great for forming friendship bonds) but then Ex is essentially telling OP he will only collect the child on the days it suits him? So what is she supposed to do the days he decides he can't do?
I can't imagine this working at all.
I think it's great the father is looking to have regular contact. But it needs to be on fixed days and a regular schedule that revolves around a normal 7 day week, for everyone's sake.