I've got a slightly different take on it. I wouldn't make any demands of him at all. If there was a court order for him to make support payments, I would simply file. Just as you'd file your income tax return to get a refund.
You don't owe him any polite requests. There is an ORDER he has IGNORED and you are going to ENFORCE IT. The court won't look more "favorably" on you because you asked him for it first, nor will it look unfavorably on you because you didn't. An order is an order.
There is no need to appear "reasonable"--that ship has sailed. As long as you don't ask for more than he was ordered to pay, and you don't go in immediately demanding that he be jailed until he pays up, the court will find your motion MORE than reasonable. If asked why you waited to enforce it, you could simply say that you had hoped if you didn't rock the boat he would abide by the other orders. But since he isn't, you are going to ask for what your children are entitled to. Remember, this is, essentially, THEIR money. You aren't enriching yourself at his expense. They are his children and he is legally obligated to support them.