I'm so sorry - but know that the occasional meltdown is NORMAL. Doesn't feel that way, but normal for the given circumstances. You are human.
Glad you called H. Is there anyway that you can set up schedule where he takes them more often, so you have a little more free time? I really don't think "no" is an option for him...he is still a father. And, with his year-long leave coming up, I think it's in his best interest to take them now more than he usually does.