The monorail hotels are more convenient when you have small kids, but pushing a double stroller up the ramps is enough to make me need a nap, too! Depending on the resort, the buses might be just as convenient if you won't have a car. My kids napped anywhere: stroller, bus, monorail, tram, ferry, etc. When they needed a snooze, they just went out.
The WDW Hilton's a great hotel and that's an awesome price, almost too good to be true, though.
(1) Make sure that the offer is for the on-property WDW Hilton in Downtown Disney. That Hilton has privileges such as EMH, that the Disney Resorts offer. Disney bus transportation is available, but MK is a long ride. I've never seen a $99 special at that hotel, even as an HHonors member, but the economy can make people do strange things. (There are other Hiltons offsite that charge less per night. The deal might be for one of those hotels.)
(2) Be certain that the deal's available when you're planning to visit. Cut-rate rooms never seem to be available when we're going on vacation there, lol. (Except one time when we stayed at POR, which really worked out poorly with three little kids.)
If someone else was paying for the hotel, I wouldn't choose an expensive hotel like the Contemporary unless there was a special deal, such as the Hilton offer your Dad found. Just my opinion.
I'd ask the Contemporary to match the deal, which probably won't happen but hey, doesn't hurt to ask, right? If not, I'd look into switching hotels to save your parents some money.