i have a feeling you'll save more money by simply saying home

Since they're friends, perhaps her friend knows that the OP's toddler can be extremely demanding and fears that the OP would have a difficult time handling both children at once? Plus. We don't know how old the other child is and also might need extra attention? There's more to this story that's not being told. OP is getting "paid" to do a job. It's not like it says they're friends that switch off and watch each others kids as a favour for free. If that was your child and you were paying a babysitter, I bet you'd want the best care for your child.

A possibility might be the friend is a protective new mother who has a newborn and she is afraid that your child might expose the newborn to toddler bugs before the baby has had all their vaccinations. If that's the case, why would you become miraculously germ free as you walk in the door? Another reason, she may be hoping to use you as a bit of free housekeeping as well. I've often heard with nanny's, some parents sometimes try to sneak the doing the dishes and laundry into schedules. So if you take your kid along, you may not be able to do that.

You put on "my" twice

I wonder if we have all the elements here. One of my closest friends has 3 young boy (6, 3 and an infant) and as much I like my friend, I find her kids pretty badly behaved, the eldest particularly because she believes in “no punishment” education. Meaning that when the kid does something naughty or starts being aggressive / insolent, she tries to talk sense into him by explaining how much that hurts other people’s feelings. She will not do time-outs, no-TV/dessert-tonight, etc. They usually don’t give a damn ( and why should they in the circumstances?). It came to the point that I don’t invite her at my place anymore because they smash everything. I prefer visiting them. It is possible that OP’s kid is like that and it’s always hard for the parent to realise it. My friend was told by her own parents and her last au-pair (who left because she couldn’t handle it anymore) that the kids need more discipline but she doesn’t accept it. If however OP’s kid is well behaved and gets along fine with the other one, then her friend must probably have a hidden reason for this unreasonable request.

You may as well pick your kid over hers. Either way you won't be making money.

Hey OP with the neck scar needs a job. Maybe he can watch you kid for you

Do the kids have a hard time getting along? That's such a strange request for your friend, especially if she expects your keep babysitting her child.

Maybe your child is a bad influence on hers? I have a few friends with kids who constantly complain to me about friends/family member's kids who are brats and don't want them around their kid.

Your friend shouldn't pay you babysitter wages when she wants all the perks of a nanny.