Please stop sneaking out...the long-term issues are not worth the short-term gains. When your daughter realizes you are not there she probably panics a bit (she may keep it to her self) which can re-start the cycle of problems.
Next time she is going to school try these things:
1 - talk about school the day before and what kinds of fun things she does there
2 - make sure you maintain her "normal" morning routine on the school day but talk about school to get her focused
3 - saying good bye to the house, favorite toys, etc. but letting them know she'll be back may help - our son had to wave bye bye to his stuffies and kiss the dog and give him a treat before we could leave for school
4 - when you get to school make her arrival and your departure as quick as possible...it would be great if you could talk to your friend/teacher ahead of time and say, "Here's the plan..." THIS IS GOING TO BE VERY HARD FOR YOU...settle your daughter in with whatever you bring to school (change of clothes, snack, etc.), give her a hug & kiss and tell her you'll see her later. She will cry. Hand her off to your friend and LEAVE!!! She will still cry, she may try to grab you but you are the mom and YOU NEED TO BE STRONG! She will stop crying, she will have FUN and you both will be better/happier campers!
5 - When you pick her up, try not to make too big a deal about your return. Focus your energies on her - ask what she did today? Make a HUGE deal about any projects or things she learned. Tell her you are PROUD of how BRAVE she was to stay at school even though mommy wasn't there. Tell her about the REALLY BORING stuff you did while she was at school!!! Talk to her about doing this again next time. When your daughter is out of earshot check-in with your friend/teacher to find out how quickly she adjusted and how to tweek the approach next time.
It will take a few tries but eventually school will become part of the weekly routine. She will cry less. You will feel better. You don't want this to continue at Kindergarten and 1st grade where you will not be allowed to hang out with her. You need to give her the tools TODAY to cope with a lifetime of changing schedules that sometimes involve long separations from mommy.
When you leave home without her and she is with dad - dad needs to take charge and say mommy has to do "X" and she'll be back. How about you and me go play with "whatever is the coolest thing for her right now."? Don't make a big deal about departures and returns and she will not make a big deal either.
Every now and again my little one still cries even if I am just running out to the car and will be back in 5 seconds. They are emotional beings just as we are and they can understand much more than we give them credit for so try to explain more and guide more and worry less!
You're obviously a great Mama so get out there and be a great Mama!!!
Hugs & good luck!
- J. :)
P.S. Let us know if next week is better!