I'm in the same situation. I'ts annoying. It makes me feel like a prisoner in my own home when they are here. Meanwhile, BM swears them to secrecy over everything in their home. DH wasn't even told that their stepfather moved out until months later (at which point, he figured it out because he hadn't seen stepfather's car at the house at dropoff in a long time). 

BM only wants to know because BM is insecure. Don't discuss anything important with DH that you don't want getting back to BM because even if you think skids aren't listening, they likely are. Outside of that, just live your life. Who cares if you went shopping, bought a new x,y,z, ordered take out instead of cooking, etc. You can't prevent skids from telling BM anything, so just roll with it. 

Our BM used to (and still does to an extent) grill SS9 after every visitation. We used to get page long emails that we called report cards, outlining everything that SS told BM that happened during our parenting time that BM disagreed with. We got emails about SS having dessert after dinner, SS staying up past 8 pm, SS getting a sunburn/bug bite, SS playing video games, my parents accidentally saying "Hell" in front of SS, BM disagreeing with us traveling a few hours away with SS to visit family, etc. Yet our BM kept her life a secret, even when it impacted DH or SS. We didn't know BM was dating GF until BM told us she and SS were moving out of state and we didn't find out they were moving until right before they moved. This was something that significantly impacted DH because it made the then court ordered visitation schedule logistically impossible, yet BM didn't think DH needed to know. It was all a big secret. 

Ultimately, it's none of BM's damn business what happens on our parenting time and our judge told her so. Your DH tell your BM the same thing or just continue to ignore her. 

They are being rewarded for it in some way. It may be in obvious ways with gifts or privileges, or in subtle ways like more attention from BM. It could also be that they can see it makes BM happy when they tell her things about your household, so they do it simply to make her happy.

She is may be outright encouraging it, or it could be subtle. She asks what on the surface are innocuous questions, then acts happy when they provide information - so they do it more.

In your case, she is doing it so she can use the information against you. You are in a tough position.

BM is weaponizing the skids against you and their father.

Ignore the "report cards." IMHO, your DH needs to have an honest conversation with his kids. He needs to let them know that whatever they tell BM, causes drama for your house, and puts DH in the middle of it. It sounds like they stir the pot and exaggerate the stories. SD11 does the same. 

Maybe I was out of line for going about it this way with SD. But I confronted her head on when she came back to our house (this was a couple of years ago). But I was pissed! All kinds of false allegations and things that frankly weren't her business. Like if I was on birth control or not. Seriously?! I flat out told her it was rude to ever ask ANYONE that and it's not her or BMs business. I told her all she is doing is stirring the pot on both sides and making everyone upset. Of course her crocodile tears came soon after. I didn't care. 

Obviously BM doesn't have a life if she is trying to decipher what you are doing with your kids. She's definitely insecure and bored. Be amused that your errands around town are her form of entertainment. Lol. 

They are spies for bio mum. What we wore, said, did or went is all reported back to bio mum like they're being interrogated with no respect to our privacy and marriage. 
 

they have learned from bio mum to not respect boundaries and privacy and so I refused to be present at any meets or events they are at. When they have nothing about us to report there is nothing to report to bio mum. 
 

my husband actually told eldest sd that by her own words their bio mum abandoned and neglected them and they had a real opportunity to build a relationship with me and our 2 kids (their half siblings) but they burned that bridge multiple times and need to realize that when bio mum dies (as she claims she's about to die from her imaginary illness any moment) that they will have no one there for them if my husband is no longer alive. Thats their future and legacy they helped create and they will be on their own with no support.

even then there is no change because they're selfish self centred people who do no respect others and genuinely spend their times guilting people with the "i'm a child of divorce syndrome" and milk it for what its worth

"It's been brought to my attention" HA!!!! BM used to LOVE to say this line before every stupid assault on us. Fascinating how they all use the same verbiage. Ignore the whore. My Skids use to literally go thru their dresser drawers while on the phone with her and tell her every item of clothing they had in our home. I nipped that in the bud real quick. We never discussed anything of importance with the skids in our home. They reported EVERYTHING back to her and it always followed up with a phone call or rambling text.  She's nuts, ignore it.

We had similar stuff with the kids.. a combination of them not having much filter.. not understanding the issues that they were potentially causing.. and pumping for information by BM.

So, we did have talks over the years about how each household deserves the privacy to live and speak freely without fear that things will be repeated in the other home.. and when things are repeated.. a lot can be lost in translation and create confusion and upset.  We did stress that we are not asking them to hide anything important from their mom.. but especially if they were upset about something that happened at our home.. that they needed to come to US.. not to BM.. because she doesn't have any authority over the house and while it may make them feel good in the short term to vent about the unfairness to her.. it results in a much bigger blowback than they probably realize and it's unfair to us and to their mom to rope her into these issues... that are quite frankly none of her business.  Their father parents as he sees fit during his custody time.. and Mom is able to do the same barring actual abuse and making you clean up your room is not abuse.. having a talk about your poor attitude is not abuse.. not buying you that north face jacket is not abuse.

Time for some fun with the little failed family spies.  
 

Photoshop vacation programs, expensive new car invoices. Expensive jewelry receipts, etc... and seed them around your home.

Load them up with bullshit that they can run home to mommy with. When she goes screaming to court and puts the SpySkids in the stand you and DH can honestly say that you never bought any of those things.

You can refuse deposition and just cut to the chase in court.    What about her deposing you cost you $4K?  I would sue the shit out of her for harassment and all related costs.

Unfortunately we all suffer that to some extent. I would like my life to be completely private from BM but have to accept that my SD16 has no loyalty (to anyone) and takes photos, videos without permission (and often without knowledge) and also eaves drops on private conversations. SS15 is fine, he is respectful of both sides although probably has more loyalty to us.

You just have to change your behaviour somewhat ie careful what you say around them and if they ask questions that you know is their mother asking via them then just tell them it's none of their business - that's what I do. We also wait until SD16 is not home to have any sort of private conversations or if that's not possible then put white noise on loudy and speak softly ha ha. 

As for the small stuff, what we eat, do etc I've had to let that go. It's further worsened by the fact that my SD16 lies constantly or at the very least exaggerates so nothing she tells BM is 100% truth anyway but BM is so naive and stupid she believes it all!

My SS12 talks soooooo much garbage about his bio-mom. She's an EOWE mom. I assume he does the exact same about us at their house. He's the all around drama queen of our house and reads the room very well, and always wants to start a conflict. I'm suffering right along with you.

Everything here gets reported back to the BM that has my 12 yo step 2days a month.  It infuriates me and I feel a shadow over me all of the time.  I actually had it.  The other day she's on a video call w/ the bm walking around and showing her the house .. my cats.. etc.  I flipped ... how are these women still so invtrusive after years and years is beyond me.  I cannot stand it... I told my DH I am sick of living under a microscope... Im so done w/ it all.