I would let mom know that you can do it on a TEMPORARY basis. I can almost guarantee that when you are, indeed, at full capacity during the week, the last thing you will want to do is take in kids on the weekend too.
It's my understanding that weekend care is more expensive, I would do whatever your rate is time 1.5 or 2. I would probably do hourly, as well. I wish I could help you on the rate... but I don't even know what I would charge for that!