How much "me" time should a SAHM have?

Currently, I am a stay-at-home mom. I spend every waking moment with my two-year-old, except when she has visitation at her father's house. She goes with him every other weekend from Thursday night to Sunday night. Other than that, she is with me 24/7. It's been like this for nearly a year now and quite honestly, I'm going crazy. Six days out of the month just doesn't feel like enough "me" time. I was thinking of taking one day each week and taking her to her drop-in daycare from 9-4 so that I can have that day to myself. My mother has also offered to take her one evening each week so that she can have a special night with her grandma and I can have a date with my friends or fiance. I'm just concerned that that would be too much time away since she also has those weekends at her dad's house. I don't want her to feel like mommy doesn't love her or is trying to get away from her, but I desperately need some time to turn off "Mom" mode and feel like my own person again. How often do other SAHMs have free time?