..She did pay for two seats so she did not invade the space of the person next to her. I have been sitting by people who were much more over-weight and did not feel obligated to purchase an extra seat. I think she was very socially responsible..
I agree the other passengers were inconsiderate, but I wonder a couple things: If Mom didn't really need all of the extra seat, why not place son there? Most kids don't mind being "uncomfortably close" to their Moms. Also, if, as it appears, you are a family member, wouldn't it have been better to switch with the child and put him next to one of you as a last resort?