Why should I have to work more hrs just so he can do less?
Why should he have to work full time so you can continue to do less? Going to Secondary School means they can travel to and from school with their friends, so no school run. They're old enough to cope with being at home for a couple of hours before you get in from work. They can manage school holidays without burning the house down.
Seems a fair enough swap for the future - you increase your hours and he knocks his back (especially as increasing age makes him statistically less likely to be able to pass the medicals or manage the heavy physical side - you wouldn't want to be in a position where he fails one and you then have to take any full time job/shift work you can get to cover the bills).
Your issues over housework and sandwiches are irrelevant in that respect - if he doesn't feel the need to make sandwiches, then don't make them. He's already said he doesn't care whether he has them or not, so it's not such a big deal to him that you object to making them in the first place.
What hours are you doing if he picks your DD up from the school where you work whilst you're at home? They sound pretty short (and inherently low paid) - why not, when she is at Secondary, look to increasing them so you are working until, say 4pm? She'd be able to get home by herself at 11 years old (or might not even be back until later, depending upon her finishing time at secondary). During holidays, it wouldn't hurt her at 11/12/13 for you to go to work and come back just after 4.
And it might feel a bit fairer at that point to him as well - if you're working more - to do more housework; I certainly wouldn't feel the need to do more if my OH was at home before 3 and refused to make it possible for me to have even a similar number of hours and kicked up a fuss about making me lunch when I really didn't care whether I had one or not .