It's hard to think anyone could be so clueless as this: I think we need to draw up a contract or for future
Well, of course you have a contract where you set out expectations and responsibilities.
You also make it clear what you are paying her for, and the situation regarding holidays
left everyday after 3 hour
Where did she leave, if she was minding them in her own home?
I think you've changed the story to suit the replies you've got about nanny / childminder.
It seems like she actually has been minding them in your home. The description of going back to childminding after losing her job doesn't sound likely at all
We thought in good faith she would help more during that time but she didn’t.
But it doesn't work like that. You specify the responsibilities and that's what she's paid for. No good faith needed
It's clear this is a close relative - your mum? Sister? - that you've an ad hoc, unofficial arrangement with, instead of formalising it appropriately.
Time to find a new minder, properly this time.