Why are you asking his permission? Since you are doing all the housework, it's your decision. TELL, don't ASK, that you are hiring a cleaning service.

If he objects, write up a list of chores and ask which ones he is willing to take off your plate. Tell him if he can do at least 5 hours a week, then you won't need to hire the cleaning service.

Also, consider changing jobs so you CAN work part time. It's not your fault your hubby is a workaholic. Let him do what he needs to, don't nag or complain, but make it clear that YOU need to spend more time with your child and that this is what is best for the child. Then figure out a way to transition to a part time work schedule.

If he is unhappy, point out that your child's well being is more important than buying more toys. Try to strike a balance, a compromise - but make sure the priority is what is best for the child.