Many cars are like this. The slide bushing takes up the slack between the bracket and the alternator housing. With 21 years on it, it is probably galled into place. This slide bushing is really tight on the bracket to begin with. You have to rock the alternator from side to side to get it loose. Swinging it around the bushing does no good.
BTW, an '87 Colt Vista is the car of your dreams? C’mon, your dreams are worth more that that.