Don't let anyone make you feel guilty for going to work. Better to have a mom that works than to have to go without!
Sneaking out of the house is teaching her that she can't trust you to be there when she expects you and will cause her to be clingy. She is in a developmental stage where she is learning to remember things/ people when they are gone, and expecting to see someone and not finding them can be very upsetting.
Find the book "the kissing hand" and read it to your daughter often. make or purchase a small purse and and put a laminated picture of yourself in it. Create a routine with her in the morning. Always follow it. It could be as simple as singing a good morning song and pouring her cereal. Tell her you're going to work and you'll see her after school, you love her, kisses! and bye- bye! Don't turn around and don't let her see you upset by her tears. You will teach her that she can trust you by being consistent, you teach her confidence by giving her routines, and you build a stronger bond by showing her you love her and will always come back to her.
Good luck and keep us posted! :)