D.D.
I think you are just wrapped up in being a perfect mommy right now. You know what works best for your child and feel that she's under stress when you aren't around. To say she hates going to daycare is quite a strong statement. Children at that age are just into routine so going to daycare 2 days a week means her routine is being changed which is what she's reacting to. She doesn't hate it; it's just different.
No one will replace you in your daughter's life. What you need to remember is the more people she loves and who love her will make her a well balance person able to make those important connections with others.
How are you have fun without your child? Well you had fun before she was born. Being a mommy is important but it's only 1 hat to wear. Putting on another hat like being a friend and hanging out for a couple hours will help you to be a better mom. Please let others take over and bond with your daughter and relax and have fun. It'll do you both good.