You have late fee in contract and now learned lesson that you have apply it first time, every time. It hard for parent understand why you suddenly charge when for longest time you have not. You must respect your own contract if expect client to respect it. If anything in your contract you not willing enforce, then remove it because it degrades contract value.
In your contract, you say you have ability to term immediately. I would be clear to these parent if they late even one time in notice period, then you will be charge late fee and you will also term their contact immediately and no care will be available to them.
Do not extend anything now because it would like your your objections which caused the notice to be very petty if you enable the same issue for rest of time this family with you.
Be very clear to them, their pick up time is 5.15pm. Be there on time or not come back.