Well there are lots of Meet and Greets there
On a serious note, I have a two year old twins. Mickey's Clubhouse is a huge hit for my kids, especially since they watch it. My daughter really liked the Beauty and the beast show, but she loves dancing and music. Both my kids favorite ride (along with mine) is Toy Story, but make sure you get to the park early and get a fast pass for it, as the waits are awful. Other ones that were OK for them but not ones they loved (but they did like) was Little Mermaid and the Muppet show. You will mostly end up on the left side of the park since the right side is the thrill rides (other than B&B and Fantasia).
If you like thrill rides, then after your toy story fast pass will allow you to get another, get ONE fast pass for Rock n roller coaster and tower of terror. Then when one of you goes into the FP line, go up with your child and ask for a rider swap pass, which when your spouse is done, you then can go into the fast pass line. Only issue is finding things to do with the LO while the other is on the ride. You don't have enough time to get anywhere and do things. So maybe mealtime might be a good time to do this.
Try to get to Fantasia early to get a good seat, my daughter loved the show, but was a little concerned for Mickey in some parts. I just told her, don't worry, Mickey will be back and be OK and when he showed up, I pointed him out and she got all excited.
There is less to do in Studios than there is in the other parks for a two year old. But I have gone several times with my LOs and have had enough to do.
On a side note, I see you are from St. Augustine, how do you like living there? My one nurse for my son takes small vacations there and is seriously thinking of moving there because she likes it so much. Her and her husband are younger (mid-20's) and eventually want to start a family. So is there a lot to do there once living there?