So far day 2 has not gone as well as day 1. :D He went on the potty multiple times yesterday and I think his only accident was during his nap in the afternoon, but even then it was right at the end after sleeping for 2 or 3 hours.
So today, April slept in while Parker and I ate breakfast and played a bit. For whatever reason, I couldn't get his potty timing right. I'd put him on and he wouldn't go, so we'd jump off and 20 minutes later he'd pee in his underpants. So I'd change him, and we'd sit on the potty after another 15 or 20 minutes, and he wouldn't go. So then we'd jump off again and sure enough, he had another accident. We went to go get his hair cut (but the hair cut place was closed), so we went to the park and brought his little portable potty chair. Again, he didn't have to go, so we played at the park until he finally went pee in his underpants again (while saying, "Uh oh...."). It seems like I was 15 or 20 minutes off no matter what we did.
After a few loads of laundry, he's now trying to nap and April has had him back on the potty successfully since we came home. So far she's about 7/7 and I'm about 0/5 on the potty training. Go me! :D
Update: So Parker is asleep for the night and he had multiple accidents and multiple successful pees on the potty. So it was a so-so day today (definitely not as good as yesterday!) but hopefully tomorrow is better! Still no poop on the potty, but I think we'll work up to it as he gets more comfortable peeing on the potty first.