Yup, just what PPs have said. You sound spoilt and entitled.
As for nasty comments - you called your Mother 'unbearable' 'unkind' and a 'bully'...
You clearly posted on here to get wave of support for you against your Mother who, surprise surprise, isn't thrilled her adult, married daughter and her family have invaded her home without any timeframe or plan to move out.
Did you expect everyone to suggest she move out of her house so you can live there with your family?
Turns out your Mum has not only spent her own adult life bringing you up and making huge sacrifices for your education, she's also helped you buy your own home, has put up with your whole family invading her space and now is paying the school fees for your child - up until the age of 18, I assume that you'll expect her to pay for your second child too?
I'm just failing to see what sacrifices you have made at all?!
You're even bringing a second child into the mix!
You didn't admit or entertain the fact you re clearly able to sell your London house and buy a flat?
Or was that a sacrifice you didn't want to make for your children's education?
Your expensive education didn't seem to teach you to take responsibility for your own life now did it?
Grow up and cut your coat according to your cloth.