W.C.
There is no way a 10 year can be left alone by himself, esp with two younger children. He would not be able to take appropriate responsibility for himself or the younger ones at that age, and they are too close in age for him to assume the needed authority, have appropriate judgment, or to expect obedience. There is no WAY I'd leave those children alone for "a few hours on the weekend", much less on a constant and consistent basis in order to work. They absolutely need appropriate child care (read: certified adult). The average age a child can be left ALONE (not in charge but by themselves) in most states is 12. In KY it's 14. The Tennessee Council of Juvenile and Family Court Judges states:
"There is no legal age for children to stay at home alone. Parents are advised to use their best judgment, keeping the child's maturity level and safety issues in mind."
As an added thought - are there TV's, cable, and/or internet in your home? Have you considered how easily a child can access/watch inappropriate or even pornographic material, especially if there's not an adult around to care for them?
If something were to happen to your children, you and your husband would be legally (not to mention morally) responsible. If something were to happen to someone else, or another's property due to your children, you and your husband would be legally responsible. I'd highly suggest disregarding what your husband WANTS and attend to your childrens' NEEDS. It sounds like you're there, but need some support. Get some statistics, information, and local/state laws regarding this subject and present your argument to your husband (I'm assuming he's also all 3 of the childrens' father?). Gather child care information you would seriuosly consider (inhome or after school care, etc) as well as the details of that care (who would be in charge, how much it will cost, the effect on your schedules and your lives as individuals, parents, and as a family). If he continues to disagree then he's obviously more concerned with how much money he has than the safety of his children. If chilcare is such a financial burden, you may want to consider if it would be advantageous financially to simply stay home, considering the change in tax bracket, etc.
All in all, tho, your children are not old enough to be home alone. At all.