financial responsibility

Hello

have 2 childern one 18 one 20.  The 18 year old has just refused to go back and finish their A levels and the 20 year old after much discussion has started at university

I have a shared mortgage with my ex - I am being told this arrangement because we cannot agree between ourselves has to remain in place until the 20 year old finishes uni and that if the the 18 decides at a later date to go into full time education then we cannot sell the house until the youngest finishes his education

is this correct -any advice