Okay, there is a bit more going on here. I'm going to be quite frank, but only with the intention of helping you. There is a problem here that you aren't standing up and saying what you really think / feel to the employer. As I recall you had the same problem with parents when you were a childminder.
You absolutely need to say to the mum what you have expressed here in a civil, polite, but firm manner. This is what I would do:
1- make a list of the things that were discussed in interview, and hence you would expect to be in the contract (hours, pay, duties, etc.).
2- Draw up a sample rather generic contract (the one on nannyjob for example -- but don't yet incorporate your list).
3- When you arrive at work monday morning, mention to the mum that youvwould like to talk to her about the contract when she has a few minutes, say sometime before the end of the week.
4- Bring your list and contract to the chat with the mum. Present the list and say these are the things as you understood them. Ask if she agrees. Then offer to draw up the contract for her for her to then approve/edit as she see fit. Or, if she wants to draw it up that's fine (really it's her job to draw it up, but you offering to draw it up for her might speed up the process).
Then, give it a week or so before youraise the issue again.
Whatever you do, do not keep quiet. It will eat away at you, you willbe unhappy, it will show at work, mum will be unhappy. Not a good situation.
This is certainly not beyond repair, but it needs addressing.