Is it not the case that, if the cleaner stayed, she would be TUPE'd across to the new contractor ?, if not, then in your T&C's on this particular contract, do you not have the standard condition that, should the client terminate the agreement and retain the existing staff, your compensation is 6, or 12 months salary ?, or even 3 !
Seems like in all these cases, if they've decided to change their arrangements, there's not much you can do about it, but hopefully, your T&C's have given you at least some recompense.
and yep, I would ged rid of her off the other contract !