it's a LOT of walking for little feet. miles. a stroller can be helpful, but also a pain... you can't take them on the train, you can't take them in line, and you can't go inside most buildings with them. so really, you are only going to use it for walking from one part of the park to another. SO... my recommendation is bring a baby carrier for your 15 month old so she (he?) can be held hands free in line and inside rides and stores. it's more practical for naps too, so you don't have to just sit for an hour or two and do nothing-- they can nap in the carrier while you have fun. (i made a simple mei tai in an hour or two-- just a rectangle with straps and is my very favorite carrier ever--i've tried all of them. my daughter lived in the mei tai when we went to disney. she was two months old. but it works great for her now too, and she's almost two. also love the t-shirt slings i made by just cutting off the sleeves and neck off two t-shirts to make a tube that slips over your head and one shoulder. use two to spread the weight evenly) also a leash would be a good idea-- that's around the age they start running away...
for safety reasons, put a little sticker or tag or something in your kids shoes or backpack with your name and cell phone number so if they get lost they can give it to an employee and they can find you more easily.
if you have kids that are too young/short to ride they let you all wait in line together and switch off watching the little one when you get up to the ride so you don't have to split up or not get to ride it. i forget what it's called... but it was great for space mountain and a few others like that.
i personally think waiting for hours in line to meet cinderella, mickey, etc is a big waste of time and money. you paid for the rides, not a picture and fake signature. but some would shoot me for saying so, do what you like... one recommendation i've heard if you really want to meet the characters is to do the character breakfasts. you can meet all the characters and not wait in long lines...
also. you can buy souveniers and mickey dolls lots cheaper off property-- at wal mart and souvenier shops. or online later. disney stores are a ripoff, and then you have to carry them around all day at the park too.
the parades are a great time to ride your favorite rides without long lines. the fireworks are too, but i wouldn't miss the fireworks-- they are the some of the best. the parades, on the other hand, are kind of... well....let's just say i think going five times in a row on splash mountain is better.
in the bibbidy bobbity botique they put some sort of glue product in your girl's hair-- her hair will stay for more than a week with the princess bun and hair do. at the end they say bibbidy bobbity boo with a magic wand that has glitter that sprinkles all over her. bring her favorite dress up to wear for it (unless you want to spend $50-200 on a dress there. the dresses they have there are really nice, but verrry expensive!!)
i'm not sure why, maybe to make the rides seem more fun, but waiting in line is very boring. i don't know why they don't have interesting things to read or games to play while in line. so get a mental list of all the "i spy" and other games or things you can do while waiting, or else you will have a miserable day. the rides are only a few minutes long, you will spend most of the time standing in line.... just prepare for that so it's not a shock.