I'm glad you've noticed that scented air "fresheners" do nothing to get rid of the underlying problem. They also contain highly toxic ingredients, and make some people (including me) quite ill. Most scented candles also fall into this category. I would never want to expose a child to those cheerfully-advertised horrors.
I've used a terrific non-toxic product over the years that can be sprayed on surfaces and into the air. It's called Smells-Be-Gone (google for sources). It's so effective it can even significantly reduce skunk odor (I used it on a badly-skunked cat). It's great in stinky garbage cans and diaper receptacles.
Other great cleaners and de-stinkers are vinegar and baking soda (but use them separately, or they will foam copiously and neutralize each other). Both can be added to your laundry (vinegar is surprisingly effective as a fabric softener!), sprinkled or sprayed on moldy surfaces, and used in solution to clean floors. B-soda is excellent on carpeting. An open bowl of vinegar in a musty area is reported to help, but I've never tried that one.
Bac-Out or other enzymatic treatments can also be effective. Use in cleaning solutions for carpets, pour into drains (which can smell pretty awful, if you check), and on pet or kid "accidents."
Mustiness can originate from mold and mildew growing in walls and floors. If surface treatments don't help your problem, you might need to investigate behind all those nice, clean surfaces to really beat the problem.
And of course, ventilation is always helpful. Good luck. This can be a tough one.