Actually from what I heard and from my experience - Leather seats are easy to clean and the cotton ones cannot be cleaned. As far as the heat is concerned - your dad is right. But I dont think that should be a big deal if you have your AC on.
Another point is - if you have a kid or a pet, it is advisable to go for leather seats. Plus Leather ones give the premium look and feel. I dont think there should be much of a difference in the comfort.
And your Mother's idea is pretty good
. I think the towels will add more cushion and will protect the seats as well. and they can be easily removed and washed
. Plus white car white towel!!