My 95 had a similar factory alarm, and it used a little chip corresponding to the unit under the seat... I had 2 remotes, and when one had the battery die, I switched the chip into the good one and it worked fine. I would ask a local bmw dealer what your options are.
Mine didn't do any of that fancy stuff, it was just a 2 button flat rectangle. I think one armed/disarmed, and one was the panic button.
My 91' came with a viper unit, so i'm a bit fuzzy on how the old one operated, sorry!