Sorry but you are out of luck, no such law applicable in a private residence. If this issue was important you, you should have only chosen a rental property that forbids smoking. Until you are the owner of a property you can't make the rules. Sorry
"My question is, what should I do?"
My advice to you is to look up New Jersey state tenancy law regarding a landlord's obligations to make sure all tenants respect the rights of the other tenants. There are two issues here that need addressing:
1. washing clothes between 1AM and 5AM.
This is a violation of your right to peaceful enjoyment of the premises and your landlord has an obligation to order the offending tenant to refrain from creating such disruptive noise during this time.
2. cigarette smoke seeping into your premises.
Allowing a smoking conflict to continue unresolved may expose a landlord to legal liability and your landlord will need to appreciate this fact. For example, in 1991, a Massachusetts woman sued her landlord because she was constantly exposed to a neighbor's secondhand smoke. The case was settled for an undisclosed amount (Donath v. Dadah; see Sweda, 1997). Similarly, a year later a tenant who was suffering from smoke coming from a lower apartment sued their landlord in Oregon. A jury, finding the landlord guilty, reduced the tenant's rent by 50 percent, and awarded her payment to cover her doctor's bills (Fox Point Apts. v. Kippes; see Sweda, 1997). There are numerous more current settlements.
If the tenant in your building is permitted to smoke then the landlord cannot tell the tenant not to. However- the landlord is required to make sure your apartment is safe in terms of security and health and that you are not unduly disturbed because of the activities of another tenant. In terms of health this would come under what is called "warranty of habitability". There are things your landlord can and should do to make sure cigarette smoke from other suites or locations is not seeping into your apartment and he must make sure he is doing everything possible to minimize if not eliminate it.
Though it comes down to the other tenant's right to smoke in his own apartment, you too have a right not to be affected adversely by the activities of another tenant- this includes the hazards posed by second hand smoke. This again would come under your right to peaceful enjoyment of your premises.
Saving the health of someone else's child in this situation is not your concern. You are not the parent so stay out of their business. Protecting your own rights is your business.
I would advise your landlord in writing what your 2 main concerns are and request a written response how he intends on dealing with this issue. You may have to follow this up with a second or even third complaint if you do not get satisfaction. What you want to have is evidence that you have voiced your concerns not just once but several times. If he tries to blow you off then you will need to escalate the issue by telling him you will need to take legal action to have your lease terminated and to seek punitive monetary damages. He may not like this because he may well lose in court.
You will need to defend yourself vigorously with the second concern. An alternative would be request that your landlord relocate you in another part of the building where this will not be an issue for you.