Hm....so your BFF isn't working right now because she's recuperating from a work injury. And your SIL cuts hair 10 hours a week. So both of them have a heck of a lot more free time on their hands than you do. It's pretty natural in a situation like that for them to start spending more time together and hanging out a lot.
Is your SIL probably doing this to get your goat? Probably.
Is it working? Yes.
I think the other poster's suggestion to make clear to BFF that you expect things you say to her will be kept in confidence and not shared with other people ...that is a good idea. It's something that anyone would expect of a BFF, but this way, there won't be any possible misunderstandings between you and her.
I have a couple of close friends who are stay at home moms and they have a similar schedule to that of your SIL & BFF. They will see the kids off to school, then they spend a couple of hours at the gym. Then meet up with a friend at Starbucks and talk for an hour or 2. Then maybe go to the gym again. Then pick up kids from school, feed kids dinner, etc. I also have stay-at-home mom friends who are much busier than that (i.e., more than the "gym & ladies who lunch" bunch)...volunteering, kids' activities after school, etc., etc.
Sometimes...perhaps this is some of what could be going on with your SIL...occasionally...you will run into a person in the gym-and-lunch bunch who has so much mental free time on her hands that she turns into a busy body. She becomes someone who stirs the pots, spreads a lot of gossip, talks behind other women's backs, etc. I've occasionally run into women like this and, in my opinion, they're a little nuts. They need a hobby...something that will take up some mental free time so they don't spend so much of their time in a negative space inside their heads. One such woman once told a group of us moms, "Today, we are shunning So-and-So. So nobody's allowed to talk to her when she shows up, ok?" I thought, "OMG, are we 13 years old again? Who says that?"
I have 1 SAHM friend in the first group who is so bored that she goes to 3-4 exercise classes a day. And she hyper-analyzes everything that other moms, her kids' teachers, and her kids' coaches say to her. Hyper-analyze to the point of 'He/she said this, but he/she said it **THIS** way. Why would they say it THAT way? What do you think he/she meant by that? I mean, are they trying to say that I'm ___? I can't believe they'd do that! I'm so insulted! I can't believe him/her!' All in the course of a minute or 2. SAHM friend & get together for coffee once every few months or so because our schedules are so out of sync with each other.
People like this...and people like your SIL get themselves really worked up over stuff that, in the grand scheme of things, really doesn't matter that much. But they can't see it. They can't see the forest for the trees because they are inspecting the nuances of the bark on the 1 tree that is 2" from their faces.
Then on the other hand, you have the full-time employee people. Let's say you & DH have kids. I do. I work full time outside the home. I simply don't have time in my life for nonsense like the middle school drama your SIL has drummed up. Why? Because my day M-F goes something like this:
5:40 am - wake up, shower, get dressed
6:00 am - get kids up, make them breakfast, load cars w/stuff
6:35 am - DH & ODD leave to take her to school
6:55 am - YDD & I leave to take her to school
7:35 am - I drop off YDD (we live a long drive from the school)
7:55-8:00 am - I get to work
8:00 am - 4:00 pm - I work a full 8 hours, eat lunch at my desk.
4:10 pm - leave work
4:30-4:35 pm - pick up YDD
5:00 pm - arrive @ ODD's school to pick her up
5:45 pm - we get home. I make dinner. Kids write their HW assignments on the white board in our kitchen.
6:30 pm - dinner is done. Kids start HW.
7:30 - 8:00 pm - DH gets home from work. He eats dinner.
8:30 pm - kids usually done w/HW by now. Kids shower, pick out clothes for next day of school, watch TV
9:00 pm - kids in bed
10:00 pm - DH & I go to bed.
You know what my day does not have time for? Leisurely chats at Starbucks or over lunch. 2 hour trips to the gym. Heck, ANY trip to a gym is not in my schedule right now. So yeah, I've drifted away from the Drama Llama Ladies Who Lunch crowd because, well, life got in the way. But I do not miss it one bit. Nor will you.
Eventually, your BFF will return to work and SIL will find a new victim to glom onto. Eventually, your BFF will realize that SIL is not someone she can trust. For now, perhaps she has to learn that the hard way. So since BFF & SIL appear to be friends, that means that you can no longer confide in BFF about your SIL's manipulative, passive-aggressive tactics. You will need to find another sounding board for that.
Everything will work out in the long run. Perhaps just not how you want it to right now. This might seem like a super duper big deal, but it's really not. Just be careful to not wrestle with people like your SIL because people like her enjoy getting dirty and you'll get dirty, too.