Hi, I haven't been to Disney World before, but we're planning our first trip for October, and I've done a lot of research, so hopefully I can help you out.
If you want to do Bibiddi Bobiddi Boutique, then I'd recommend to do it super early in the morning on the first day, as according to to one article I read, it's best to accommodate up to two hours for the makeover.
Because of this, by the time you finish, a lot of the big rides may have long lines, but since you have two days and are staying late for the first day, you should be able to get rides like Big thunder mountain, Seven dwarfs mine train, peter pan's flight, space mountain, splash, jungle cruise and any other super popular rides I've missed either later in the evening or on the second day. So, after the makeover is done, if you haven't already had breakfast, I'd get something to eat at the Main Street Bakery or Confectionery before heading in line for Haunted Mansion.
After this, head over to Fantasyland and instead of doing Peter Pan's Flight or SDTM, do rides like Mad Tea Party, Prince Charming's Carousel, Dumbo the flying elephant, the many adventures of Winnie the pooh, it's a small world, Under the Sea, and if your kids especially love Mickey/Donald Duck, then watching Mickey's PhilarMagic should be good. Most of these rides should have short wait times, and you should be able to get all this done within the next 2 hours. For lunch, go to Friar's Nook, which seems to have a tasty selection of treats and hot dogs. During this time at Fantasyland, you can also do Character meet and greets with Mickey and Minnie and main street, princesses like Cinderella, tiana, and Rapunzel at Princess Fairytale Hall, Belle at Maurice's cottage, and Peter Pan near Peter Pan's Flight among others.
Once lunch is done, if you didn't do all the Fantasyland rides I listed before, go do those now, or a bit of shopping & a some meet and greets. The afternoon should be a bit more casual since you've already done quite a lot. After taking a look around Fantasyland, go check out Adventureland, and if Pirates of the Caribbean and/or Jungle Cruise doesn't have a long line, go straight to those, they are both classic rides and I'm sure your kids will love to the jokes on Jungle Cruise. Then, take a stroll around Swiss Family Tree, it's not a must do, but a great filler if you need a break from constantly running around or thrill rides. Another fun activity for the kids is A pirate's adventure - treasure of the seven seas, which is a scavenger hunt, so if your kids love these, then go for it. If you're looking for an early dinner and your kids loved Jungle Cruise, head over to Skipper Canteen which is supposed to tie up with Jungle Cruise. Then, for a dessert, get the classic dole whip at Aloha Isle. It should be a bit later in the day by now, so take your time, and after dinner head back to Magic Kingdom, and try and do the big rides you couldn't do that morning or the smaller rides you didn't get time to do. Then perhaps get ready for fireworks, and just relax, as it's probably been a full on day.
So, this is just for the first day. sorry if it's a bit messy and probably not the best, and also that's a lot to do in one day, but of course you just adjust it the way you want, these were just simple suggestions, and I'm probably not the most reliable source since I've never been to Disney before, but I hope you have a great trip and let me know if you'd like my suggestions for the second day.