Lots of questions there so let's see if I can get you some answers.
First of all you've not mentioned how many nights you're staying for but £372 does not correspond to the price of the premium half-board meal plan for two adult guests and three child guests, which would be £342 for two nights assuming you're booking direct with Disney in the UK.
I don't know if much turns on that anyway though: if your kids are going to want pizza, burgers, or pasta, then any meal plan is likely to be a waste of money. Would you spend £342 (or however much it turns out to be) on two meals out normally? (Remember that this includes one soft drink per person only, and wine is extra too.)
Half-board premium gives you access to the top tier, best of the best restaurants such as California Grill, Inventions, and Auberge de Cendrillon. The vouchers may also be exchanged for admission to Buffalo Bill's Wild West Show. At most table service restaurants they give you the choice of anything off the menu. So they are good if you enjoy table service dining in a relaxed environment and don't want to be limited by the choices on set menus.
It seems to me however as though you would get on better with quick-service or buffets. Prices at quick-service are €11-15 for an adult meal (main course, side, drink, and perhaps a dessert) or around €7 for a kid's meal (same ingredients but smaller portions). At most buffets it is around €30 per adult and €15 per child, including a soft drink. So that will come in quite a bit cheaper than the meal plan and I think you'll probably enjoy it just as much. Remember £1 is around €1.36 so you'll get a decent deal on the exchange rate too.
I can't really say much about Café Mickey from direct experience, but I expect that like most of the character restaurants, the experience will depend on how busy things are. The characters can ordinarily only spend a minute or two at any given table because they have to get through everyone. The food seems middle of the road but I would expect most of the price is paying for the characters — so as it costs around the same as any other table service restaurant, I wouldn't expect gourmet dining or anything in the same league as Walt's: an American Restaurant or Bistrot Chez Rémy. As between it and Inventions, you're probably paying about €60 more for your party in Inventions but you're guaranteed to find simple food like chicken nuggets and pizza on the buffet.
Finally, then, if you do go for the premium meal plan, make sure you get full use out of it by going to Inventions rather than Café Mickey (which is a Plus tier restaurant), and try to get in Auberge de Cendrillon if your kids would like to meet princesses. Just remember to book your restaurants ahead of time as they can get full.