As you have a contract for services, such things are often signed by both sides. If the original was thus signed, I would consider the original contract stands - not any verbal discussion implying a change. Does this original contract include a clause outlying the amount of notice you must give? - if it does and you gave this notice, then I don't see how she can charge you within the terms you describe.
Retention - irrespective of whether it could be considered within the contract you have (had) or not - is surely a red herring. Retention applies if you take the child away (for a holiday perhaps) and she has no child to look after for a temporary period. I don't see how she can claim for a retention (even if one did assumed it WAS part of your contract).