Is the Moh’s plus 1 supposed to be included in wedding party transportation?

I personally would talk to her and ask if he could be included. My husband and I just had our big wedding 10/2 and we provided transportation for our bridal party AND their partners. Some chose to drive separately which was perfectly fine, but we did offer for everyone because I personally would want to be with my husband and vice versa. Especially since he's her brother in law.

This is pretty standard. If I were the SO other I'd probably prefer to drive separately. I wouldn't want to just be standing there waiting for rehearsal to finish or waiting for everyone to be ready. I'd rather just meet at the venue as a guest. Plus you're gonna be busy helping your sister, you won't really have time to entertain your SO.

I've been through this twice already only i was the SO and my FH was in the bridal party.

For both of them i went with him to the rehearsal and the dinner after (both dinners were very informal at a pizza place) and just hung out. For the first one, I think, everyone took their own cars and i went with him while they took photos and again, just kinda hung out.

For the 2nd one, they had a party bus for the bridal party. My FH left me at the hotel while he met up with the bridal party and I was going to take my own car to the church and reception. Luckily at the last minute his best friend who was also invited to the wedding asked if i wanted to carpool and i was super grateful that i got to hang out with him and i wasn't alone.

I'd just explain your situation to your sister and see if it's cool for him to come to the rehearsal and dinner and hang out. I would suggest he take his own car to the wedding though - that way you guys have a way to get home after everything is over. I would HOPE the bride wouldn't make a big deal. As a former shy, awkward, SO party attendant I would certainly understand if someone came to me with the same problem.