Same issue with the M113, and to a lesser extent the Fuchs. Vanilla vehicles do show a similar behaviour, but the difference is that they have a tighter turn radius which makes it more controllable. Note that boats seem to handle very differently to amphibious vehicles.

I made some videos:
https://youtu.be/rpDy-cPcPuE
https://youtu.be/hu1C2GQUW1s

Here's some videos for better reference concerning the AI handling. I suppose after testing multiple vehicles together, the wheeled ones do fair better than the BMP, which seems like the only one that gets stuck. The M-113 might be the same as well. Maybe because of the tracks? I also tested the RHS BMPs to see if maybe its an ARMA problem, but they seem mostly fine.
Vanilla Control
GM Vehicles
BMP-1

Well, I am mostly unable to control this vehicles in the water. (Just forward or backward, turning is almost impossible). Same with AI driver.

Same kind of issues with PT-76. It seems that if you stop vehicle when it just enters water and hatches are opened, it many times get stuck and won't move at all or moving very slowly. Same can happend when entering from water to land and stopping on point when hatches are closing. Maybe that is issue that vehicle cannot move on land with hatches open and cannot move on water with hatches closed and now vehicle is half in water and half on land and got stuck? Seems to work fine when entering water or land with speed and not stopping on water line.