If you google the phrase, perhaps you can find some material to print out and show your mom, so you aren't being the bad guy.
This is called third hand smoke. It is dangerous.
The residue on smoker's clothing and skin is dangerous, it does not have to be the actual smoke. As Ellena says, let the pediatrician tell your mother, ask her to come to the appointments. SIDS risk goes up when babies are around smokers, even if the smoker never smokes around the baby. Please take this seriously and nerve yourself to tell your mom. Let the doctor bear the bad news if you can't.
Nicotine can be absorb trough the baby skin, my husband smokes but never inside the house only in the balcony. He always wears a jacket and wash his hands, forearms and face with soap, after he sanitize them and brush his teeth. I don't like the cigarrate smell so i asked him to do that so in one appointment the pediatrician told him and he told her my wife already ordered me the same, probably you should take her to one of baby's appointment and make sure she knows there is a small risk. Good luck mama and take care!!!
Just tell her the Dr recommend it. I smoke and they told me that the dangerous chemicals get on your clothes. I told them I smoked outside and never around my baby or children. They said that about the clothes and if asked what I could do because I do not want my kids around it. They said to where a jacket, wear my hair pulled back and to wash my hands. They also said before I breathe on baby or kiss baby to wipe my face with a baby wipe and brush my teeth. I know it sounds over board but I do it all the time for the safety of my children. I am trying to quit this time around because even though I have never had any health issues with my babies, I don't want to risk it or risk ny kids picking up the discussing habit. Good luck and just be honest with the facts with your mom and if she cares about the health of your baby She will do it with no problem.