This was a clever idea - the babies were certainly out of control. I think the difficulty was compounded by the fact that there were a lot of times where the offered items weren't needed and the needed items weren't offered. I think that makes for too much "out of control." Also, I may be wrong, but it didn't seem like losing the disguise would matter - the babies always took the items and their states would always change. Perhaps if the babies wouldn't accept the items without the babysitter being disguised then it would make sense and seem less incidental. Your game definitely has potential. I could see you scaling it up so that maybe their are different levels; like more rooms open up and the babies start roaming around. Or maybe, if the babysitter wants the bottle, it has to go to the kitchen, but the diapers are in the bedroom and the pacifier is dropped wherever the last baby was that used it? Maybe in later stages, the martian also has to answer the door - so it better not forget its disguise!
Anyways, good job!