Kat, I'm afraid that my trying to give advise in this situation is rather like the priest doing sex therapy, and I'm sure that better informed people will be here soon, but a couple of things come to mind. He has visitation rights, but she is dropping the kids off (and, presumably, picking them up again)? Seems to me that he should be responsible for the transportation, at least one way. If that might trigger his departure, she should at least include these transportation expenses in her child-care expense log. IRS rates (I just checked) are 48.5¢ per mile.

Why does she want him around? If she isn't getting the support money, and she has to tippy-toe around so the kids don't realize what a jerk he is being, perhaps it would be better if he went away.