FFS cant believe how many people post who clearly have no clue about the Tax Credits system. If Op's ex is the TES poster (which seems pretty likely, or else he is a journalist looking for opinions...either way am happy to give mine!). He is a 4th year teacher so earning about £25k. Therefore he would be entitled to a proportion of his childcare being paid (about 50%) and be entitled to the Child Tax Credit bit (currently about £50 pw per child).
The childcare is not hugely expensive for 2 children, 3 days a week IMO. 4 hours a day (an hour before school, 3 after 3-6 perhaps) times 2 children, times 3 days, is 24 hours a week childcare, at £3 an hour each (for a childminder) that makes £72 a week. Hardly that expensive. pickgo I'm allowing for work after school such as preparation and marking, meetings and parents evenings. Because that's what teachers actually do.
If I was the op's ex, paying my own mortgage or rent with no help (get a lodger? with 3 young children in the house? really?)
and caring for 3 children, including feeding, clothing them etc, I'd be a bit resentful of the op living on the £340 a week she gets, with no rent or mortgage to pay.
The fault is with the benefits system, as benefits should be able to be spilt according to care, rather than just allocated to the person who has care for 1 extra day a year. However, in the absence of common sense from the benefits system, the op would be fairer to at least allow the ex to have one of the children on his claim, if not 2.