E.V.
Hi K.! Okay, first of all, it's great that your son is showing interest in potty training and he is absolutely old enough to be potty trained. I'm a little taken aback by your mom's reaction - if she is running a daycare, that is part of her job to help with potty training while he is at her house. If she can't pay enough attention to the children to remind/help them use the bathroom, what is she doing all day? That's her JOB, that's what she's SUPPOSED to be doing!
You should definitely get some underwear for your son, Gerber makes really cute "big boy" underwear that's thicker in the middle so if they do pee in it, it starts to soak up some of it and they can feel that they are wet - in other words, it's thicker than regular underwear so the pee usually doesn't go everywhere. If that's what your mom is really worried about (getting her house messy), maybe that will help. I totally agree with you about the pullups - they're pretty much just like a diaper.
Anyway, I would absolutely start him in underwear this weekend and try and help him learn how to take his pants and underwear off and on by himself so that at your mom's house, all she has to do is remind him to go (and probably wipe him once a day!!) and he can do it himself. I assume that since she has a daycare, she has a potty seat/step stool in the bathroom. I'm not saying that it's completely the job of the daycare/preschool to potty train people's children for them, but when the kids are there all day, they do have to help a little! My son was in a daycare last summer starting right when he turned two and he was potty training at the time and his teachers told me to go ahead and bring him in underwear each morning since they were helping all the kids in the class potty train. They would take them all to the bathroom at regular intervals during the day as well as taking them if they told them they needed to go. I just brought extra underwear and pants just in case.
Anyway, I think it's great that your son is expressing interest in potty training - count yourself lucky because some kids are really resistant to it! You are doing a good job by encouraging him and helping him! Good luck with everything, it's great when they finally are completely diaper-free! Oh, and yes, he should be in a big bed. :-)