I understand it's hurtful -- but it's probably not intended.
A couple of ideas:
If you'd like to do family events, plan them. Call your parents-in-law and ask them if they'd like to go with you to XXXX and tell them you're going to invite your sister-in-law and her family as well. Then do it. Then do it again. And again. Sometimes, do it with just the parents-in-law; sometimes, just the sister-in-law. Keep doing it.
Not that it's ideal, but I know in my own family my mom is more inclined to do stuff with her daughters and their families than with her sons -- including bossing us around and even inviting herself. It's not that she doesn't love her sons (my brothers), their kids or their wives. It's just that she's closer to her daughters -- a mother-daughter thing, I guess. When my brother or my sister in law call and invite her, she goes but it is a little less easy for her. Now, this may not be as it should be, but it is what it is. And, by the way, my sister in law who lives closest to her has been part of our family for OVER 25 YEARS -- and my mom is still this way. I'm not even sure she realizes that it could cause hurt -- and God bless my very wonderful sister in law for not taking it personally.
And, lastly, deep breath here, family is under no obligation to make everything open to every one else. Several years ago, my brother and my other wonderful sister in law (I'm so lucky my brothers have good taste!) planned a big Europe trip for our families and we included my mom. With just our two families and my mom we were a group of 10 (gulp!). I didn't want to "vacation" in a crowd. We didn't open the trip up to our other siblings, as much as I love them and their families. I know they were a little miffed, but understood at the same time. My take on it was that others could plan their own great adventure. The 10 of us had a blast. So, my point is that really, not everything should include everybody -- even the big things.
To be fair, yeah it's kind of miserable that your sister in law asked to borrow your car -- that would sting a bit. Hope you can use this as an incentive to maybe create the type of relationship you want to have with your husband's family. My husband will tell anyone that it's tough to be a "married in" in a close family!
Be the change you want to see in the world. (Ghandi)