Well, actually 3 full meals and 2 snacks a day should be the norm for a growing child. My son has the same issue and his metabolism is so fast, he has to eat at least five times a day. And if he doesn't get his regular snack on time, he'll come to me and say he has to eat because his legs are shaking.. he just needs the fuel to keep up with his body.
I have children ages 14, 11, 9 and 3mos (baby) and a stepson part itme that's 12.....(5 kids at home out of 8) so I know about the food prices, we spend better than $500 a month... big time. And I don't feed junky snacks. I stock up on the large box of yoplait yogurt, large pack of string cheese, several boxes of "whales" (generic for goldfish (they are so expensive), cheese crackers, chewy granola bars, nutragrain bars (generic though), fruit cups, applesauce, puddings, fruit snacks, trail mix.... you name it, you'll find it at my house. I also get pretzels instead of chips, and I get a pack of cookies occasionally.
Is it expensive? Yes, but that's the price we pay for having children..... they just have to eat... they are growing, so I would try real hard not to get frustrated and don't cut back on their meals, just provide healthy snacks in between instead of any empty calorie snacks that will just drop there blood sugar and make them more hungry.
I do feel for you.... we're broke to, I just had a baby, I quit work and I am racking up GIGANTO student loans being a full-time student in college.... so I feel your pain.
Another option is look for local deals around you at some of the mom and pop grocery stores, buy in bulk and buy generic if it's cheaper.... I find it is even cheaper than buying the name brand with a coupon. Oh! And grow a garden this year, we are.... produce is getting more expensive by the minute!
Good luck.... we're all in this together....