My cousin is really incredibly allergic and I know that for her, she has an asthma pump in every room of the house, along with several HEPA filters and is diligent about vacuuming and dusting. She and her family has about 10 or 11 cats and while it's not easy on her, they help out quite a bit. I know that when we had a friend stay with us, we bought a HEPA filter and that helped alleviate some of the issues (but certainly not all). Another alternative might be to get a hypoallergenic kitten, but I'm not sure how feasible that is.
If having another kitten is really out of the question, then it's all a matter of keeping Mittens entertained. Lots of toys, boxes, and basic activities. When you're away, something to consider is getting a cat sitter. I haven't had to deal with this just yet since we have roommates, but if you can get either a sitter or your granddaughter to come in and not only feed him and change the water, but to get in some solid play time, then perhaps it would be okay?