Heath, I feel so bad for your children. If that’s your attitude about them, then the courts are probably right for giving your ex-wife custody. A father doesn’t want to support his children? Are your kids just the sum total of how many mitzvos they do?
I’m not sure your arrangement during your divorce or what your ex-wife wants. But the non-custodial parent is responsible to contribute to the upbringing of their children (man or woman).
As to my friend – they knew that they could reasonably accomodate her. If she hadn’t switched with the Catholic woman, she could have switched with someone else. People often switch days where she works, so they could reasonably guarantee her the right to switch. Again, I don’t know what industry you are in.