Lola is spot on. Your daughter is not happy that you have been absent (has there been more than just the one business trip?) and that grandma has been in charge of her. Some of the acting out and unhappiness is inevitable as she tries to adjust. Some of it could be exacerbated by perhaps Grandma having different rules than you do when you're not there. From experience with my own daughter (who is a rule follower and does NOT like to get into trouble of any kind), know that, just because she does what Grandma tells her without backtalk, etc.. doesn't mean that she LIKES what she is expected to do. She may also very much resent Grandma doing things with her that YOU used to do with her. Are there "special" things that you once shared that now Grandma does with her instead? Of course there are. You may not think of them as "special".. but that is how it is perceived by your daughter, particularly now that it isn't just you and her. Grandma (in your daughter's perspective) is interfering in your relationship.
Please be sure (if you aren't already) that you take time to spend alone with your daughter daily. Have time that is just you and her, no grandma. Bedtime is a great time for this. Have her say goodnight to grandma out in the living area (not grandma coming into "her" bedroom)... then you and she go snuggle up with a book for her bedtime ritual... just you and her.
Also... if Grandma is now her caregiver (and is unemployed)... she probably isn't spoiling her like grandmas tend to do, and your daughter is probably accustomed to from her grandma.
I know that my kids' attitudes toward my parents changes when I have left them in their care for a day... totally different than when they are visiting only and aren't the "authority" in charge of them. And actually, so does my parents'! (They are less tolerant).
Perhaps you and your mom need to sit down (privately) and discuss "parenting" strategies and routines. Make sure Gram isn't being more strict than you think. No matter how much we love our kids (and grandkids) I think our tolerance for them is used up faster as we age.. unless your mother is a TOTAL and COMPLETE SAINT!
I am only 40, and I have less patience with 3 & 4 yr olds, even 5 & 6 year olds than I did when MINE were those ages... and it wasn't that long ago.... mine are only 8 & 11 now. So perhaps letting Grandma have a breather from childcare (when you aren't around) - if it's possible - might help some too. Be sure that your daughter gets to participate in playdates and other fun activities that she was doing before Grandma arrived.
And keep praying.