If one more day per week in daycare would decrease your net take home to 200 per month, you have the wrong job AND the wrong daycare. I know that working is also an investment in your future as you build your reputation at work and your resume. But being away from your child this much for such a small pay off is just crazy.
The first thing I think you need to do is make sure you are maximizing the childcare deduction. If your employer does not allow this deduction at pre-tax dollars, then you need to look for a job that has this.
Find an in-home caregiver that charges less than the center, but still has certification, years of experience, and or whatever you want for them to. Your daughter would still have friends and can still be learning. But you can keep a bit more of what you are earning.
Also, could grandma do more than 1 day per week? Your daughter is feeling that way because she's not there very much. My grandson and I are extremely close to each other. And yet, when he's away from me for 2 or 3 days, he cries when he's left. He is fine though right after. I can't even imagine him being upset enough to throw up.