Is the Contemporary Resort or the Grand Floridian worth it?
For a family with children ages 4 and 2, in your opinion, is it worth the money to stay at the Grand Floridian or the Contemporary in order to be easily transported via monorail with an unhappy/tired child?
That's a hard question to answer. For 99% of America the answer is a huge no it is not worth it to stay in the Contemporary Resort, the Grand Floridian Resort or any other of the Disney Deluxe Resorts. They just cost too much. The average cost of a monorail hotel is $500.00 per night. That's just outrageous.
If you are part of the 1% of America that can afford a big vacation or if you save up knowing what your vacation will cost then yes, a monorail resort might be for you. If being to your room in 10 minutes versus 20-40 minutes is important, then yes, you might want to consider the monorail hotels.
I love the Disney World monorail and I love staying at the monorail hotels, especially my favorite, the Polynesian Resort. It's even more convenient than the others because of it's proximity to the Transportation and Ticket Center and the Epcot Monorail. But for my last 2 trips I stayed at the Pop Century. Why? Because the Polynesian Resort has become too expensive for me.
Disney doesn't have any problems filling the monorail hotels so I guess their not overpriced, but they have become too expensive for Dad. If you can afford it, then absolutely it's well worth it. There's nothing better than being close to the parks. However, if it's a strain on your family, don't worry about it. It's not that important.