Re: Mum has lung cancer
When my Grandma was diagnosed with lung cancer she stopped smoking immediately, having been a smoker for 55 years. I insisted that no-one smoke in the house, and people stopped smoking around her. She was having treatment for the cancer (and thankfully her recent scans have come back clear!) and we wanted to make sure nothing nasty at all got on to her chest.
It is different, of course, in your case, but if I were you I would stick to my guns and ask him to go outside. It will be much more comfortable and be a much nicer environment for her to rest in if she isn't surrounded by second hand smoke, and having stopped smoking it will be much easier on her if she isn't around smoke.
I think you're definitely right in this situation, so don't give in!