I would not pretend to be qualified to advise you. I can tell you what I might do?
I have an 8 year old daughter who can be "choosy" the one thing she does like is steak...very rare(juicy), which, I might add, she cooks herself.
I would encourage a 10 year old boy to cook his own hamburgers/hot dogs/fries even pizza....some people make this a family affair..puting their own topping on a base.......you of course would have a lo-carb alternative base.

Hamburgers are easy, with the pattie that you have previously prepared with egg an lean minced meat....My brother has 4 boys (10years-18months) they all love Auntie Liz's hamburgers, 2 of them have a slice of cheese and the eldest likes one with the lot..egg, bacon cheese and pineapple( I use the canned p'apple slice through the ring, now you have 2 thinner rings and VWWWWWWWAALLLLLAAA!!!!!!!!!!!!! )

OR, If your boy enjoy yukkie things (as some boys do)..he can even mix up the egg and meat...with his CLEAN hands, of course,....VERY YUCKIE.
I pretend to be grossed out by the mixing process and they find this funny..really funny. Your 10yr. old could be reacting to dad's condition..if he is close to his dad then maybe he could help ....pooooorrrrr mum who COULD be having difficulty working out "all this diet stuff" . It's amazing how they rally........if only for a little while, that gives you time to "cook up" another plot!!!!
Good luck ....please let me know how you get on.
Liz