Just go.
If you don’t put your foot down now, they will continue to control all your choices going forward as they already have indicated their intention.
You need to show them you can make your own decisions and take your own actions.
It's better to have them onboard and supportive but if they are going to be inflexible, adopt their strategy and be equally demanding.
You should be able to study where you like and live away from home as an adult.
An 18 year old can vote, marry, join the Armed Forces, drive a car etc.