Hi M....I live in Auburn too!
It isn't because they go to daycare. Both of my two oldest boys potty trained at 2 years 6 months exactly, wearing underwear day and night. I homeschool, they've never been in day care let alone 'babysat', but a few times that I can count on my fingers.
My girl will be 3yo next month and shows no interest at all. She doesn't care if she pees on herself. So, she is not ready at all. I'm going to try again after she turns 3yo next month.
Kids are different. They're ready, when they're ready. My boys, I taught them to sit down and go potty. No use giving them all the rules at once! lol. I also bought a lot of hot wheel cars and put them in a bag and let them have one every time they went potty. With my oldest, I had to set a timer, because he drank so much and couldn't hold himself for long periods of time (not that they should anyway). My 2nd son could hold it longer (still can, which isn't good for UTI's), so he didn't have to go as often.
Hopefully my 3rd son will be easier than his sister...oh I can only hope. Good luck with the potty training.
Now, as far as the sippy cup thing.....there is nothing wrong with your son still using a sippy cup. Our boys still used them when they were 4yo and up! Could they use a cup without a lid? Yes! BUT, we didn't want them roaming around the house without a lid on their cup! Our kids learned to drink out of a cup without a lid about 18 months old. But, they still used a sippy cup when going about the house. Our 3yo girl right now, drinks quite well out of a cup without a lid (she gets ours all the time), but when she is done drinking, she loves to pour it all out, if we aren't looking.
That could be one thing that they are just wondering about..if he can drink out of a cup that doesn't have a lid. Our kids learned in nursery at church at 18 months old when they went in. The nursery would have little tiny 'bathroom' cups half way filled with water. They learn.