As a dietician who studied children's eating habits, patterns, and requirements - your son does NOT by any means need 3 bowls of cereal followed by toast, much less then asking for more food.
I think reading between the lines your problem lies in that DH seems to be taking the 'give him what he wants' line...as long as he eats it. This works...up to a point, and is usually only recommended for children before they reach age 3 as all toddlers go through a fussy stage.
Is he just 3 or nearly 4? As they near reception, children should be growing out of their food phobias/fears/eccentricities and conforming more to adult patterns of eating (of course there always will be picky eaters!)
Grapes and bananas are fabulous snacks, so do keep those up, and if he's recently started preschool or upped his hours, it is very likely he's more hungry after this time.
How are his sleeping patterns? Allow your son 1 bowl of cereal and 1 slice of toast with topping for breakfast or some fruit, or all 3 if he is particularly hungry.
But if he doesn't eat his standard 'meat + two veg' or seem as though he's getting enough protein or veg into him, do not give him sandwiches or extra fruit to top him up. If he truly was hungry...he would eat the meat & veg. You do not need to worry about starving him at this age, although he WILL dig his feet in more than a typical toddler for 2 reasons: 1) You (and DH) seem to have differing views about the food he eats, and he senses this conflict, you've also in the past give him 3 bowls of cereal, so he WILL kick up a fuss for it, just expect that! And 2) He is 3, not 18 months, so his will is going to be a lot stronger.
Most children who are 'chubby' at this age will even out by about age 6, but if not, it's nothing to worry about until it starts to affect other areas, such as sleeping, concentration, mobility, and energy levels.
You sound like a good mummy - just remember that whenever you or DH thinks you're 'depriving' him of food, he doesn't need 3 bowls of cereal!