Because of the in-laws we have done 2 day trips to Disneyworld and it can be done
Personally, if you are looking for deals and just one day in the parks I would probably stay off site. I mean why spend money if you aren't going to get the advantage of hanging out at the hotel. I also hate the transportation at the resorts, so for me I would stay off site and just drive in. I agree check out Disboards for help with finding good offsite hotels. Magic Kingdom is the best park for that age, so I would stay there all day, they tend to have the longest hours too.
As for the parks you might be super surprised what your 17 month old can do and will want to do. My DS was pretty much raised at Disneyland, had his first trip to Disneyland Paris at 19 months (he is getting ready for his third trip next month), and first trip to Disneyworld at just over 2 years old. He loves the parks that might be because he is so used to amusement parks, but he always had a blast! Rides like Dumbo, Small World, and even the tea cups are huge hits with DS. Watch out for some of the fantasyland rides, some are darker then you might expect and can get scary. If you aren't sure about a ride, check out the ride along videos on youtube. You can see the whole ride inside, and prepare a child for what they will see. It helped get DS over his fear of POTC, he loved the ride but hated the drops (WDW only has one)
I agree a carrier is a great item to have on hand. DS would nap in the carrier and we would go on rides that might scare of bore him, like Haunted Manison or Carnival of Progress. We found carriers so much handier, since strollers constantly have to be reparked, get moved by cast members and if little one falls asleep in it, your stuck. The carrier you just keep movng on
Money saving tips, bring snacks, bring refillable water bottles, pre-buy small toys cheap and then just get one big item, share treats and plan at least one splurge.
ETA: With younger kids plan to go slow, but I think WDW has a area the kids can run around and play, it is never a bad idea to give them a chance to just run and play, to break up the time, otherwise they get really bored in the ques.
Oh and the baby care center is great! They have changing tables, nursing stations, baby food to purchase, microwaves and more. you won't need all that but still thought I would mention it, since most of them are great. I love that they usually have small toliets too.