Family dynamics being what they are, it is quite possible that OP has seen the difference in personality traits of the twin cousins, and is privy to the feelings of the twin with less “muscle” in that relationship. Just as in the womb, where one twin can grow larger and have received more of the space to grow, there may be a ‘larger’ personality - the recipient of the energies and thrust of the dominant parent, and with the stronger social skills and charisma.
OP cousin may be intimately aware of the stress this has placed on one or the other twin, and is seeking to advocate for quiet cousin at this one juncture when, for the first time, the twins can get out from under mom’s steering.
There’s no entitlement that obligates parents to fund “dream school” any more than there is an entitlement that obliges parents to buy a “dream car”.
If the parents are paying, then the parents have ultimate veto power. Nothing is stopping your cousins from self-funding the school of their own choice via merit scholarships, ROTC, their own savings, etc.
It’s true the twins should try and talk to their mom. Help them speak their minds. But they should also be open to what their mom will say. Because believe it or not, a mom’s instinct never fails. There might just be something more that the peace of mind she wants to get.
If family is seeking FA, it might possibly get a more generous deal from the same school, as compared to two separate schools.