I've been with my girls a couple of times alone--if you can handle a crowded mall with your kids--you would be okay in the parks. If your 4 yo's are inclined to wandering and disappearing in public places--then a 2nd adult would be most beneficial. My personal experience is that I can handle my children in a public setting b/c they are not prone to this type of activities or other misbehaviors. They love going "bye-bye" and know that should they not behave, they get removed immediately from whatever place we are at. My friend on the other hand has a real tough time with her kids at the store--but she takes her kids to Disney no problem. You really have to know your children and what their behavioral strengths and weaknesses to know whether or not you can handle the parks solo. There are plenty of single parents out there who just do not otherwise have the option and they go to Disney without a problem.
My girls are now 4 and 1 1/2--so the only toughy is that little one is too small for Goofy Barnstormer, other than that--we were okay. You just have to have a different game plan all together and realize that you probably will not get to ride your rides (i.e. Space Mountain or Tower of Terror or RnR). I say this b/c it will be safe for you and your kids--just not sure I would brave a baby swap with my 12 year old--it is all up to you. Safe for the 12 yo to ride alone, just worried about the other way around. The height for Splash and Thunder Mountains is 40 inches and DD4 is just shy of that--once she is tall enough for that it will once again become difficult to go solo as little one would be unable to ride.
I will advise--that our first trip solo was a bust--dd4 had developed a fever in the park and it was rainy and miserable. A subsequent visit turned out much better. Of course, the first visit was spur of the moment and the latter visit was better planned.
My personal opinion is that MK is the easiest park of all for the kids as it is totally kid focused and most attractions are suitable for little ones, Animal Kingdom perhaps would be not as busy, but navigation is a tad more difficult, MGM is not my favorite park any more but they do have kid shows--but not really any kid rides, EPCOT--I love it and my kids enjoy it when we go, but it does ring potential boredom--ways to liven it up--allow the kids to play in the splash fountains (not the big one, they have other ones where water comes out of the ground), decorate masks in the countries, visit the finding nemo exhibit at the Living Seas--et cetera.
Happy trails!