:O You should be looking after your children at night. Your helper is not on the clock 24/7. She should finish at a certain time (usually 7 or 8pm) and start again at a certain time (usually 7 or 8am). Being tired because your children kept you up at night is one of the joys and responsibilities of being a parent. Suck it up.
We handle the kids in the night. My helper wakes up at 6am to help my daughter get ready for school and she's busy around the house till around 8pm (with breaks in between when the kids are at school)... I feel she needs to have a good night's rest of at least 8-9 hours.
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I guess, at night you should share the responsibility and should not leave the kid entirely to be looked after by the helper. And if it is too taxing for you all then you can send the baby to the daycare for half day.
We have opted for daycare in the day, so the helper can rest and she takes care of the kid(s) at night so we can rest.
thanks