I did not see the OP discouraging the cousin from visiting, only from staying in her home overnight when she does. She mentioned two things that would make having the cousin staying in her home difficult, the fact that she is a smoker and that the OP‘s mom is already staying there.
As someone who is allergic to tobacco smoke, I understand completely about not wanting someone who smokes staying in my home. Even if they smoke outside, smoke will linger on their clothes and can come in around doors, windows, and through the ventilation system. Smoking is a hard no for me when it comes to visitors.
As the former caretaker for my parents, it would have been a huge burden for anyone to visit and stay in the house with us (other than my sister who helped with their care). Even when things are going well, the added stress of monitoring the well being of someone every minute of the day is difficult at best. To add a visitor who needs to be fed and entertained on top of that is exhausting.
Neither of these reasons has anything to do with keeping the cousin from visiting, just finding her an alternate place to stay. There is nothing wrong with setting boundaries, and it is easier on both sides to do this from the start.
When I go to visit my sister, I always stay in a hotel. I like having some time to myself, and I don’t want to inconvenience her by staying in her small home. We spend plenty of time together while I am there, but I think if you asked her she would say she appreciates that I stay in a hotel. She has never asked me to, and she does have a guest room, but it simply feels more appropriate.