I know how challenging those can be!!!

If it is like most windshield mounts that I have encountered, either a ball and detente socket, or a hidden latch, the answer is simple, even if the operation is not.

The ball and detente style just requires someone to give it enough of a jolt to get going. The trick is to get it going in the right direction, without damaging it or the glass. That method will have to be left up to the operator, but nylon tools (even make-shift ones) are likely preferable. Soft or Hard wood can be used as well. Be inventive, but careful.

The hidden latch presents 3 problems. First, finding it; Second, figuring out how it releases; and Third, the same problem described above. That being to get it moving in the right direction. Mirrors, precision screw drivers (to poke into any crevice, crack or hole), even old used dental picks can be useful. Study the attchment first, then attack! (Carefully, of course.)

Fortunately for you, you have another example mirror mount to go by. At least you know which way to push the old one off by looking at the tracks on the replacement. You may even be able to determine which type of latching system it uses by that same piece. Check it out, then ATTACK! (Remember your nylon tools!!!!)