Did you perhaps put the nestbox over her chosen potty corner? This is a common mistake leading to this behaviour. If so, transfer the kits to a different nest box (so no urine odours remain) and put it in a different spot in the cage.
If this it not the case, the problem is more difficult. You are right to be concerned for the kits, as they can get chilled if wet. You could remove the nestbox at night and put it back in the daytime. That might help. You could also try giving her a litter box (a dollar store plastic dishpan will do with some shavings or straw in it). If you add a bit of her urine (soak it up with a paper towel) then she may start using the dishpan instead.