S.H.
I DO know what you are going through, I've been there. I'm not a single mom, but she's totally mommy's girl and I didn't leave her for more than an hour for the first 2 1/2 years of her life. I couldn't. My husband was not available due to work for those years.
My thought is this: Maybe she just really does need you right now. How long has it been since her dad left the picture? Was she ok with separation before that? Does she legitimately feel insecure? Could there be anything at your parents' house that makes her feel insecure? How old is she?
Some kids are just clingier than others and it might take her a while to grow out of it. She might experience a huge surge of stress hormones if she's not with you for a while, which is normal in a lot of (even newborn) babies and young children.
I know it is hard and I know you need a break. In the four years of parenting my daughter I've never spent a night alone. She's super clingy and it has driven me crazy sometimes. But looking back at the times when it was really difficult, I'm glad I chose to stay by her side when I did and I have some regrets about when I did not.
Take heart in this: You're a great mom. She adores you.
How about a little daily "alone" time at a gym which offers child care? Good luck.