on somebody'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!
on somebody’s ˈhands
1 (of work, etc.) to do: I’ve got a lot of work on my hands at the moment.
2 that somebody is responsible for: I’ve got the neighbour’s children on my hands this afternoon.