We milk our goat twice a day, and the kids are still on her. We do not remove them at night, and she always gives more in the morning anyway - we didn't want to have the kids and the mom bawling all night, since we live in town. We do not supplemental bottle feed the kids at all. We do give them fresh veggies, and the kids started eating hay, and nibbling at the mom's oats by the time they were 1-2 weeks old.
The biggest issue is going to be feed. A mom with kids, and milking takes a LOT of feed. If you can feed her enough, she can produce even if nursing kids - you'll get 1-8 cups a day, depending on the goat type, how many kids she has on her, and how much you feed her.
Best if you have lots of forage for her, plus grain her twice a day. The amount of grain will depend entirely on how much forage or fresh veg you can give her.
If you milk once a day, you will get less, and it WILL be harder to keep things going. She'll dry up sooner. But you can still get enough, for long enough, to make it worth it.
Milking twice a day isn't that awful. We still sleep in for an hour on Saturdays, sometimes we are late milking them at night (I mean REALLY late), and they put up with us. If you have a goat with a large udder and are maintaining peak production, then timing of the milking is important or you'll end up with a goat that is in pain if you go much past milking time. But if your goat is not maintaining peak production, you have more flexibility.