Yes - I have done it many, many times and we always have a blast. I started taking my kids solo when they were 2 & 4 and its been wonderful. Sometimes DH joins us for part of the trip other times we go alone. When you think about all the time you spend with them doing grocery shopping, going to the zoo, mall, park etc it's really not that much different.
You will find that you can ride all the attractions appropriate for a 3 & 5yo as three to a seat so that's no worry. The parades can be tricky if you stake out a spot and then someone has to go potty. Sometimes a kind neighbor would hold our spot, other times we foud a new one or just did something else.
I highly recommend staying onside - use ME to and from the airport and you will only have to worry about having fun with the kids. We usually had cold breakfast in the room, did our big meal as table service lunch and counter service for dinner. This gave us a nice break in the afternoon, good food at lunch prices and my dd's were more likely to sit through lunch then dinner.
I find going on their pace and doing what we want makes for a wonderful relaxing vacation. Even though your the solo adult your not cooking, cleaning etc so you can really just focus on having fun with the kids.
At that age I used an umbrella stroller for the 2yo around the resorts and to and from the parks and rented a double in the parks. It was much easier to get the umbrella on/off the bus with the two kids then my double.
My dd's are now 11 and 13 and due to school and outside activites our "girls only trips" are less frequent but we are doing part of our April vacation solo as DH dosen't have as much time off as we do.
If you have more specific questions or concerns please let me know as I have probably done it on one trip or another
TJ