Are the ex wife and bio mom the same people?

Your DH shouldn't be responding to her BS at all. If there's something legitimate to discuss, that's one thing, but not that a kid won't do his chores.

We're e-mail only with BM, so we filtered all her e-mails into a folder that we check periodically.

I would block her from your phone all together.

Maybe you should start answering his phone and say he's busy and may you help her. If she gets into petty shit with you then you remind her of her call being irrelevant bs. Call her out. Or suggest her emailing him. If her bs calls gets to much then block her until it's his weekend then unblock,

Been there and solved it BUT my case was really REALLY BAD!
BM was calling every other day, texting 4-5 times a day, emailing daily. Calling from the bar drunk on weekends, stealing my mail, showing up unannounced and walking into my home, and stalking me at night, would literally park in front of my home for 20+ minutes.
If DH ignored her, she would call nonstop, then call the cops to "check the house" police were stopping by to "check" all the time.
This went on for YEARS, DH thought it was "normal"
(Even though my ex didn't act like that)
I filed for an RO after the county sheriff's department issued a no trespass on her for the stalking and illegal entry into the house.
VERY VERY FEW of her calls/texts/email were about the kids, NONE were urgent issues if they were about kids and she demanded an answer NOW!
My suggestion to you, have DH explain to her it's disruptive and that you will take legal action to stop it such as a CO with communication limits if it continues. DH also has a communication CO in place now for BM limiting her to email only unless it's an emergency.
Good luck.
P.s. start recording in a notebook all the calls and texts and emails so you can track how excessive it is

First of all, she should not be calling you AT ALL.

Second, if she's been doing it for this long, she is getting something out of it. Your husband is responding enough for it to be worth it for her. Or she likes knowing that is causes problems (neither she, nor the kids, should have been told this). Or both.

He needs to not respond at all, unless it's truly important. He should not respond to tell her to stop, he should not argue with her about it, nothing. Actions really do speak louder than words.

Both of you need to stop answering her calls and texts all together. If it is an emergency she can leave it in a VM and your DH can decide if she needs to be called back or not. Do not let her control you guys like this. It's like having you both on a leash. And it is not OK.

BM is super high conflict and eaten up by bitterness and jealousy . She constantly texts DH to bait him into arguments since she thrives on drama . DH ignores her 99% of the time but in the evenings , his constantly lit up phone got on my nerves . He now turns the phone off when he is home .
I will not allow crazy to invade my home via text. Anything he needs to discuss with her must be done between 9-5 when he is out of our house .
She never texted or emailed me personally since she knows I would rip her a new one immediately .

It sounds like BM may need help dealing with kids. She might expect your DH to be helping her deal with some of these issues -kids not listening-Kids not contributing to house work- whatever the issues are, it sounds like your DH you and her need to sit down and discuss discipline options for the kids so all of you are the on same page. I don't know how often your DH has his kids, and I don't know what the exact situation is. I am a BM, also my spouse has a son of his own. My ex and I are constantly in contact with each other regarding our eldest son who is behavioral-problems at school consistently- and if I cannot deal with something I text my ex and say" Can you make it to the school to pick up our son" because I work fulltime and so does he, we have to now take turns dealing with school matters.I took over a year off of work to attend to my son and stay at school with him and I was always talking to my ex about the son and what was going on because we had appointments each week. My ex husband wanted to be involved in everything with our kids. Our son has a possible disibility and we work through a local center so I rely on him for helping me a lot and taking turns taking him to special appointments and also I expect him to support me when I am having issues with him- if he is grounded from the WII for two days, I let my ex husband know so he is not going over to dads house and playing games.