I have always refused to attend training days on non-work days, whether FT or PT, in a professional environment or a supermarket job. I have never been sacked for it. 
My ONLY option for childcare is formal childcare, not enough CM's local to me, and the formal childcare here is not at all flexible either, due to being so oversubscribed. If, like me, you are a Lone Parent with no family back up, you just CAN'T be flexible like this.
And in the OP's situation - I wouldn't be able to either.
But then, I've never signed a work contract without getting my employer to remove any clauses that pertain to flexibility around work patterns or training days.
If you can't be flexible, you can't be flexible.
And as for the poster who is being expected to magic childcare arrangements on days off to fit in around her bosses childcare arrangements - SOD THAT. I would refuse. Not MY problem that him and his wife will have to arrange childcare. I am assuming it is one of the bosses usual work days, on Mon/Tue/Wed? If not, I can see the issue, if you never work even one day a week together, but if that's the case, why do the bosses childcare issues take precedence over the employee's childcare issues?!