It sounds like you need to come up with a combination of things to keep her busy. Here are some suggestions:
1-2 days per week, have her go to a friend's house to play, at least for half the day. If you can have her out of the house from 9:00 - 1:00, or 1:00 - 5:00, you can get a lot done during that time.
1-2 days per week, let her have a friend come play at your house. If she has someone else to entertain her, she won't bug you as often. You'll be home so the kids will be supervised, but you can get a lot done while they play.
Does she have a best friend or two? If you can trade off with another mom, you can create a great schedule. Mondays, she visits friend A. Tuesdays, friend B visits you. Thursdays, friend A visits you. Fridays, she visits friend B. The other moms will probably also appreciate the break!
Another idea: have you looked into camps through your city or local community center? My son is going to a day camp this summer through the city that is only $18 per half day. So even if you did five half-days per week, it would only cost $90/week and you'd get your mornings or afternoons free (full days are available at $36/day).
Another option is to hire a mother's helper. This is someone too young to really be a babysitter, but old enough to keep your daughter occupied and entertained while you're also in the house. Usually someone about 10-12 years old is perfect. You can get away with paying only $5-7 per hour. It's basically a playmate, but someone who can also help get snacks and help your daughter pick up her toys. At that age, they could play in the backyard by themselves.
Also, I'm not sure if you are divorced or separated, but is her father giving you any form of child support at all? If not, get a lawyer and make him pay.