A few other considerations- car ins? Clothing budget (as a Mom, I know those little ones outgrow things in the blink of an eye!). I agree with some others that groceries seem REALLY low for a family...is that a number you're hoping to hit or anywhere near what you're spending now? I also don't see any savings allotted for, yet the expenses you put forth leave an unaccounted for $500+ each month.
If you're truly finding that money is tight, the 'date night' and 'fun money' portions seem excessive to me. I agree they're important things to acknowledge for sanity's sake, but could date night be $20 for a pizza and a movie rental once the kids are in bed?
It feels like there's a lot of info missing to make a solid plan. But once you truly have all of your categories together, you can sit down with a calculator, pen and paper. Weekly expenses come out of your paycheck and into your envelope each week (assuming weekly pay), once-a-month expenses or 'sometime' expenses are factored in either in chunks as you have money not allotted somewhere else each week, or again, divided into each week.
Budgeting is really tough when you begin, but I promise, it gets easier and eventually becomes second-nature. If you haven't read it yet, you might want to pick up 'The Total Money Makeover' by Dave Ramsey. The book is life-changing for many (myself included), and while a lot of it is truly common financial sense, seeing it all laid out in an easy-to-follow plan is less scary for many of us.
Lastly, you (and your spouse) NEED life insurance with those little ones at home. It won't cost as much as you might fear and is important enough to work into that budget.