Typically 3 year old?

I have a 3 year old wonderful little girl in my care, been here about 2-3 months now FT. We still don't have much of a connection, she's always asking for her mom and always seems sad or bored to be here. She lives with her mom only and goes between her grams house and moms house and daycare. She's clingy to mom at drop off and again all day just asks for her. I ask her if I can help with her lunch, shoes etc and it's always no, my mom will help me. I don't know if it's a phase or if she's truly unhappy. The kids are a bit younger 2.5 and younger but she seems to play well. Her previous daycare was all older boys. I'm worried about asking mom about it. Any ideas on this?

There is a lot that could be going on here..... you said she lives with mom only. Have the parents recently (and I mean in the last year or so) separated? That can really change a child's behaviour for quite a long time. Perhaps she is just a more reserved child. She just may not be a smiley and happy child. Sad, but that may be her personality.
I would probably approach mom, since it has been 3 months now (should be long enough to settle in/ adjust). Let her know that you have no issues with her behaviour, but that you want to make sure she is happy. Ask her about grandma's house. This little girl may just be super attached to her mommy, and missing her, especially if mom has just gone back to work full time recently or something like it.