That's just stupid!

Under context it sounds like you were going to her place to watch her child, if that's the case the I'd personally tell her to go f*** herself. Your essentially doing her a favor, most people don't charge a friend as much to watch their kid as an unknown babysitter would plus your someone who already has rapport and trust with her. If I was helping someone out and babysitting for them, and was told I can't bring my own with me, they would be looking for new help and told to never request something from me again and I hand out favors like tic tacs.

If it were reversed, and she babysat your child at her home, could you tell her she wasn't allowed to watch her child at the same time? That's rediculous! Tell her if it's really worth finding a new babysitter over you'll just find a new job.

Gotta say though its a shitty thing, i cant really blame your friend. Its a job at the end of the day and who brings their kid to their work place on the norm. Yes its your friend but when it comes to business that level of professionalism must be maintained otherwise it can all go really bad really fast. that being said, if you are paying the same rate or near said rate you are being paid to your own babysitter, thats a bad time investment, find another job.

id tell her find a different babysitter

don't babysit for her then, if your toddler isn't welcome as your doing your job, find someone who will accept you and your toddler ;) best of luck

just tell her that if you can't bring your kid you can't do it. an that you'll find a new job

I would inform her that your child comes with or you don't come at all.

That's ass backwords... Oxymoronic

I've seen a similar situation happen before. The person in question let their kid run around wild and break the person's stuff, the kid was mean to the babysat kid. It wasn't the kind of situation any good parent would want their kids in. Maybe it's the same here?