I'm not sure if "this person" is your husband or not. If it is, it's possible his stalking was something he only did once. Did he tell you about the stalking - admit to it or did this information come from your SIL? You mentioned that it was strange that your SIL would tell you about the stalking then invite the person he stalked over to your place. No offence but maybe SIL is the problem.
The way he behaved when you split up in the past along with his other comments would probably make me not trust him either although I think an open and honest discussion with your husband would be helpful. It might be more helpful if you both went for marriage counselling. If he agrees to it and it's what you want it could be quite useful.
Personally, I'd give him a rope and see if he hangs himself - in the metaphoric sense.
Interesting, but you married this guy knowing that he stalked someone in his past. You married him for better or worse. Maybe you need to have a discussion with him to find out where HIS head is at. Maybe he did learn his lesson, anyway give him the benefit of any doubt as if you had doubts remaining you shouldn't have gotten married.
Also in your 5 year marriage, how have things been?
People change situations change mindsets change. Keep the past in the past and don't let it ruin your future!