Crikey! What happens if you eat really slowly, does it help or hinder the situation, have you tried it? I don't suppose any diabetics are going to have any useful ideas because we get hypos for different reasons than you, and they're sorted out by eating, whereas with you it seems eating will sort it out then drop you down again. My cousin had gestational diabetes and she swore that eating a plate of veg before proper dinner would stabilise her sugars, I have no idea whether or not that would help with your issue though. I once read somewhere that there are two different types of insulin release when eating, perhaps that line of inquiry might turn up something useful? Also your liver is meant to give out a form of glucose if you go too low, I wonder why yours doesn't do that? I think that has something to do with (and this may be wrong) something called alpha cells, whereas insulin comes from beta cells. Clearly some messages between important cells aren't getting through.
Reactive hypoglycaemia sounds like the opposite of diabetes. Without medication, we have high blood sugars, so it's only once the diabetes gets treated that hypos come into play. One of you said your sugars have gone down to 1 - that's extraordinarily low. Do you carry glucagon injections in case of emergency? They're available to type 1s, have you heard of them? You might have a case for getting hold of one. Mind you it might make things worse afterwards, send you crashing again. I suppose it's worth enquiring about though. Hypos are often manageable but sometimes truly dreadful and everything you describe is normal for hypos. When you treat the hypos, how much carbs and what type (high GI or low GI) are you using? Do you eat loads because you feel so hypo or do you manage to contain yourselves to a set limit? Or does it make no difference at all? What a conundrum to be in, it does seem though as if low-carbing might be interesting to try out, one of you mentioned it above, because you release insulin in response to carb intake so in theory it might help even things out a bit? As with all things to do with sugars and insulin though, it always ends up being a lot more complicated than it seems. I wish you all well with it, I'd hate to be swinging up + down like a yoyo like that all the time, it's very wearing.
I read an article in Practical Diabetes once about this type of thing and there are several little-known reasons for people dropping low after meals (I think I counted 13), so getting past the GP level and to a specialist in the area may prove a useful move, eg a diabetologist or endocrinologist.