There are diodes in the alternator (wrapped up in a diode trio and aluminum cooling fins) that keeps that from happening. It blocks the battery voltage TO the alternator so the current only flows to the battery to charge it when the car runs. If the diodes(s) fail, the battery current can go from the battery to the alternator. This is likely what's killing your battery. It's hot to the touch because it's turning battery power into heat. It's acting as a load.
The regulator has transistors in it and diodes, and when bad, they can cause funky problems as well. Although in this case, if I HAD to bet on something, I'm thinking you got one or more leaky rectifier diodes. JMO, but I'm not a wire biter, so you better get a second opinion. Hopefully, someone here can come rescue me if I explain something poorly or incorrectly.
I hope you didn't get a Bosch rebuilt alternator. They suck donkey balls. Unless it's an injector, or a Bosch OEM part for a particular car, I'd run away from it. They suck at making parts for a G-body.
At least check this alternator out. You could put another alternator on it. Or get new diodes for the current one.
Get more info from automotive electrician folks. Don't go just by what I'm saying and just start throwing money at it. But doing an alternator check is where I'd start.
This is how I would check to see if your diodes are all ok. This may not give you everything you need to diagnose the problem completely, but it could narrow things down. In other words, if it passes the diode check, it still doesn't mean your regulator or other pieces parts aren't bad.
Turn car off, keys out, remove the positive battery terminal on the battery, and then take a multimeter with a diode setting and put the red lead on the battery post of the alternator and the other to the casing. Take a reading. You should see OL (nothing), or a very very low number of millivolts. Diodes can leak a very little bit, but they shouldn't let the dogs out. Then swap the lead positions to the other way. You should see a marked increase in the number. If this happens, the diodes could be considered good. If not, at least one diode is having problems.
Another way, is run the car and put a load on the battery, like headlights or if you have a hi-amp stereo, turn that on. Put your multimeter to
AC volts, and run the red + lead of the meter to the "BAT" post on the alternator. Connect the black lead to the negative post of the battery. If you get anything more than 1.5 VAC, your diode(s) are toast.
To test the regulator on the car when running, measure the voltage at the battery and keep it there. May have to use the clamp accessory for the meter for this. Stick a small screwdriver or metal allen key into the D shaped hole in the back of the alternator. You want to ground the brush tab in there to the side of the D hole. This fully grounds the field, which the regulator usually controls, to give you max field output. So effectively, you're going around the regulator. Don't bypass the regulator for very long, just enough to see if it's bad. If you see the voltage increasing, the regulator is bad.
Unfortunately, no OBD1 scan tool on earth will find a diode problem. It's going to be good ol' fashioned electrical gremlin hunting with an ammeter and voltage meter. For these parts I mentioned, there are no repair procedures or replacement pieces that Joe Shadetree can fix on these. You have to replace the component part if any part of it is bad, period.
If it's the diode trio, and you have a stock 78 amp 12SI alternator, then the GM part number is 1984459. (or aftermarket equivalent). They're fairly cheap, and while you're in there, not a bad idea to replace it.
If it's the diode rectifier section, then the GM part number is 1984454. (or aftermarket equivalent)
If it's the regulator, then you will need to get GM part number 1116423. (or aftermarket equivalent).
I'll defer to the automotive electronics gurus here. Come and save me.