2Nd Grader Getting into Trouble in School

Talk to her. Make a picnic and get away from the house and talk to her. You might have to do this a couple of times.
Ask her if someone is bothering her or if someone has ever told her to keep secrets (besides presents) from you. Does she talk about her Granddad? How?

Also your grounding is too severe and is making the problem worse. You do not want to lose her trust.

What my grandmother and greatgrandmother would do with my cousins and me was sit us in an approximate corner area in the living room. There always seems to be a ball around and after awhile we could roll the ball back and forth out of boredom. If someone kept the ggm would get get one from her sewing.

This is not your question, but have you looked into Head Start for your preschooler? It is sliding scale and should be reduced price or free.

You might want to confide your worries to the school counselor and let her talk with your daughter. They are trained to talk with our little ones in a manner which helps the children tell what their fears are - or just what is bothering them. Also they introduce behavior modification to the children. At that age, the children are not ashamed or feel awkward about talking with the counselor.
I am the custodial grandparent of two boys - 2nd and 3rd grade. My 3rd grader has anger issues and he has been talking with the counselor for the past two years. She has given him several ideas on how to handle his anger and frustration...and has given me some as well.

I would recommend working with the teacher about a behavior chart with rewards. This worked well with my son. The school should have some ideas on this. Feel free to email me if you want examples on how we did our behavior charts with our public school. ____@____.com