Is it your mother or your spouse's? One of you is just going to have to be direct. That because of DS' extra sticky mucus, he can be more suseptible to colds and coughs and possibly end up in the hospital, cause lung damage... Sounds drastic, but you'd all feel absolutely terrible if your child caught something that could've been prevented.
We've had issues with my MIL being too embarrassed about what others may think if we have her ask her sisters and other relatives about their illnesses. But DH has just had to say if we attend a family event and someone is sick, we very well may leave. We'd like to know ahead of time so we can make an decision. We've had too many relatives show up with "just a cold" and find out it was pneumonia. There's an uncle with COPD who doesn't come to events anymore, but we were always very worried what bugs he might be carrying.
Now it could be something as simple as a cough caused by new blood pressure medication -- both my MIL and Dad have a dry throat clearing cough which is caused by that. You could give her a call and inquire about her health, indicate that you noticed she had a bit of a cough to open up the conversation....