I know you are busy, and today's world makes it tough to balance work and home life. But if you are going to have someone come in to care for your child/ren, here are some ground rules you need to embrace:
If you have agreed to be back by 6pm, be back by 6pm. 6pm is not 6:30, or 7, or 7:45. And if you phone the babysitter to ask whether she can stay until 8 and she graciously says yes, don't walk in the door at 8:15. This is why the babysitter has said she's not available on Saturdays.
Have some food in the house. Technically, the babysitter can order pizza delivery, but given what you are paying her, she should not be expected to blow an hour's pay to buy a small cheese pizza and tip the delivery guy. Spring for some snacks.
If she will be feeding your kids, have food that's easy to prepare for them. You might even consider making some food and refrigerating it for re-heating. Otherwise, you may find that the leftover takeout Thai you were going to have has been microwaved, chopped and fed to your offspring.
Look at a calendar. See that summer is here, which means that you need to buy an air conditioner for the sweltering sweatbox that your house becomes on 80-degree days. And the kids will need summer clothes. If you don't do this, don't be surprised when you come home to find half-naked children re-enacting Woodstock. The good one.
Do NOT run out of diapers. Enough said.
BABY-PROOF YOUR HOME. If your babysitter needs to take the kids to the first floor to keep them (and herself) from passing out from the heat of your sweltering house, she should expect that the electrical cords will not be in plain sight, and that the credenza containing all of your china cannot be easily opened. The open kitchen shelves containing the glass bowls and mixing apparatuses should likewise be dealt with. The babysitter doesn't appreciate having to be creative with dining-room furniture in creating barricades, and when your children start saying "no" to everything you say, you have only yourself to blame.
Finally, as your kids get older and their language/interactive skills develop, you need to buy new toys to engage them. The same ball, plastic blocks and teddy bears don't cut it any more. These are intelligent human beings, and you need to get it together.