You've made your point with him. He knows how you feel. He can't, or won't, quit right now, maybe not ever. He's also lying to you , or you think he is, or a combination.
You can't control him. You can control yourself and your own reaction. You have some control over your children, especially the asthmatic one.
First thing: join a support group for those with addicted spouses. Learn how to deal with, and not deal with, these habits. There are things to say and do, and things not to. They can help you develop strategies, and also give you support.
Next, give him a separate, sealed laundry hamper - most hampers have some air circulation, but that's a problem in this case. It might even be one of those step-on trash containers that are fully sealed. Put it in his closet and put your clothes in another closet, even if it's in your kids' closets/rooms. Don't share a dresser with your husband. And don't do his laundry. Not one pair of socks. Label a laundry basket "Dad" and tell the kids not to go near it. If you can't stand being around him because of the smell, then keep your distance, even if it means sleeping in another room. Don't be passive-aggressive about it. Just say, matter-of-factly, that the smell is really strong and you need your rest.
Don't let the kids ride in his car. There's residual smoke in there, and there is probably tar residue on the inside of the windows. When my parents sold their house, they had some professional cleaners come in. You cannot believe the filth on the inside of the windows. It was so pronounced that my mother quit smoking in their new house.
His doctor cannot talk to you without a signed release, but you can talk to his doctor. Write him a letter about your husband's habit and the extent of it. Insist that his next physical include some additional testing for smoking-related illnesses so that cancer and emphysema and asthma are caught earlier. Most health insurance plans will pay for smoking cessation programs.
You probably should increase his life insurance coverage because he's shortening his own life. Make sure those premiums are paid off. You might take the same amount of money he uses for cigarettes and channel that into something else positive - a fund to take your children away for a smoke-free weekend (without him), or a cleaning service to come in and remove the smell from the rooms he's in the most often.
Talk to your pediatrician about other steps to take. If you can take your husband to the next few appointments (or even better, send him with the kids and without you, and ask the pedi to ask questions directly of your husband about anyone smoking in the house or car). If you're not there, your husband might be more honest, and your pedi can identify the smell of smoke in the office, confronting your husband.
It sounds like your husband started smoking as a reaction after the devastating loss of your daughter 9 years ago. Grief is a terrible thing and sometimes needs some specialized counseling. Ironically, your husband's habit is endangering the other children you have. He needs help but not from you at this point. It's also possible that, having lost a child, you are panicked about losing other children to breathing-related illnesses and even your husband due to smoking. That can be very anxiety-producing and make you hyper-sensitive to the smells, the sights and the very thought of hazardous behaviors.
There are things you can do to strengthen your daughter's immune system - I'm not sure why you have her off her meds. Did she have a problem with them or has she been free of attacks lately? You're coming into the winter with houses (and cars) closed up - so those things might flare up again. I'm not a huge proponent of medication when other things will do, but there is a use for them and perhaps you should have an inhaler or nebulizer on hand for her.
There is a new anti-inflammatory measure (all natural, well-researched, made in a US plant overseen by the FDA) that help with a lot of things including the inflammation in asthma-affected lungs. I also work with a fellow who quit smoking by boosting his immune system - he got rid of colds and flu symptoms, and felt so good he actually forgot to smoke.
So, I think, as with all addictions, you can't get the person to quit. But you can stop enabling and in a more assertive but less confrontational way.