Here's a sweet little song for Mother's Day which is quick to teach and easy for the kids to learn: "Dearest Mother, I Love You" (page 206b of the Children's Songbook). It also lends itself to very well to easy hand movements if you want to do that. Practice for a couple of minutes each week for three weeks before Mother's Day and you are probably good to go.
It makes me sad that some leaders don't want to teach Mother's Day songs in case some child doesn't have a living mother, or their mother is not "kind and true" or for whatever other reason. I feel that we should be teaching children what the ideal of motherhood is, so that if their situation isn't currently ideal, they have something to strive for in their own life. They may also see and appreciate these qualities in some "mothering" person in their life whether it is an aunt, grandma, teacher or neighbor.
Please don't deprive mothers or other mothering person the wonderful opportunity of seeing their little precious one singing in church on Mother's Day. If they don't ask you to have your Primary sing, please ask them.
You can find my flipchart here, complete with sample signs you can use: Dearest Mother, I Love You