on someone's hands

on (one's) hands

Imposed upon as one's responsibility; obligated to confront or deal with. I'd come and pick you up, but I've got Jane's kids on my hands this weekend. If the two countries don't start stop this antagonistic back-and-forth, we could have a nuclear war on our hands!
See also: hand, on

on (or off) someone's hands

having (or not having) to be dealt with or looked after by the person specified.
See also: hand, on