What you are describing doesn't sound like hypoglycemia to me. Even though there are mood swings involved, what you usually see with that is being tired, depressed,headache, confusing,blurred vision, nervousness, dizzy, sometimes they won't sleep alot, and they usually crave sweets.
A big baby is usually characteristic of someone with diabetes. If he is hypoglycemic, give him orange juice, that usually gets into the blood stream faster than anything. But I would think he would be more on the "sicker" non fighting side if he had hypoglycemia.
Why can he not snack during the day at daycare? That is not good especially if you think he has hypoglycemia. He should be eating more than any other kid in there. He should be eating at least every 2 hours if not sooner. If not,you are going to throw him into a diabetic coma. Just make sure that he is eating good stuff and not junk or processed foods. You should be able to carry things like veggies (you may have to steam then barely and send them in a container but can eat them without heating them), fruits (although you will probably want to go easy on them but he will probably still need some),beans are really good source because he really needs protein. Put them in a little container and have the day care heat them up about 25 seconds and let him eat them. They make cookies for diatbetics that you can buy now and that will be good too. AND DO NOT FORGET TO GIVE HIM VITAMINS!!!!!!!
That is probably the reason he fights eating is because he doesn't get to eat often: he gets out of the habit. I think it is hard to get kids to eat anyway.
But also, if you suspect that is what he has, then you need to see a dr because he may need medication to control his insulin level (especially if he isn't eating) and that could be dangerous if it isn't controlled properly. Get on the computer and look up sample meal plans or sample snacks and see what other ideas you can find for him but DO NOT LET HIM GO WITHOUT EATING. If it was my kid.... and I do this anyway.... I would feed him or at least offer it to him every hour. I do that to mine now and she isn't even diabetic.
I would definitely get my pediatricians referral to see a specialist.
And during church... I alway carry cheerios and crackers and things like that for mine to eat during church. Everybody else does too if they have little ones.