I am afraid that I won’t be able to give you a definitive answer to your question, mainly because the scientific facts are not clear.
What we do know is that bronchiolitis and croup in infants are viral infections – and these viruses may be also cause colds and other upper respiratory tract infections in older children and adults.
We also know that these viruses can survive on hard surfaces such as door handles for hours, especially if the atmosphere is more on the damp side.
This is the reason why colds and flu are more common when we have cold, damp winters, compared to when it is freezing and frosty.
So, on balance, my opinion (and it is only mine) is that what science tells us on this subject, in a way, supports what your mother-in-law suggests.
On the practical side, we do need dry clothes so why don’t you hang your washing in a different room from the one your infant is in?
In addition, our homes are often over-heated in winter so perhaps a small opening in one window for ten or fifteen minutes might help draw in some fresh air – this might also reduce the moisture in the room your clothes are in, assisting the drying process.