I personally am going to come down on the other side from what most of the other mothers have said, but thats my personal opinion. You need to make a decision based on what is best for you and your family.
I did co-sleeping with my son till he was eighteen months old and I really enjoyed it. I feel that children need to be loved and comforted at that young of an age. You might try reading some of Dr. Sears books on parenting and co-sleeping just to get an idea of whether any of his ideas would work for you or if you would even be interested at all.
I do understand that the 2 different ways of being put to sleep are putting you in a tough position, but if your mom is watching your daughter for free, you might want to be forgiving, or even try to combine her style and your style in some way to give the child a regular routine. Such as, rocking and cuddles for 15 minutes, then into bed.
Once again, I switched my son to his own bed at 18 months and have had pretty much no problem with him going to sleep on his own since. Sure, it was a tough week teaching him that he had to stay in his own bed, but it wasn't that bad. After getting used to going to sleep on his little mattress on the floor in my room (maybe you'd use the pack n play), with me not in the room after books and songs were done, I was able to switch him to his own bed and room with no problem at all when he was 2 1/2. He never tries to sneak into bed in the night or anything like that.
He goes to sleep on his own, stays in bed, sleeps all night, and the switch was never that big of a deal. A comforted, reassured child is usually a confident, happy, self assured child later. He is very independent and outgoing. Being cuddled to sleep did not stop him from switching to his own bed or make him a clingy "Mama's boy".
I guess my point is, once again, you need to do what works best for YOU, depending on your schedule and beliefs in parenting, but maybe you can figure out some happy medium with your mother. Changing over later to going to sleep on their own is not too hard, in my opinion.
Just wanted to add a different perspective, Good luck!
S.