I relate to your story - my SS was completely alienated from us by the time he turned 15, and was gone for 3.5 years (he's now back, which is a whole other ball of wax). So I know the pain of dealing with this, knowing and seeing where it's going.

But ...why are you emailing the attorney and talking to BM? Isn't that DH's job? If you are trying to let go, then step one is to let DH deal with his son, his ex, and his court battle.  When the writing was on the wall that my SS was going to be alienated, I very briefly toyed with the idea of becoming the intermediary between BM and DH - I was desperate.  Thankfully, people here talked me out of it and they were right. 

You can't solve this.  You didn't cause it, can't control it, can't cure it.  It's going to go where it's going to go, and all you can do is be DH's support when it goes there.  I have holes in my tongue from biting it when I wanted to ease my anxiety by asking DH about something relating to SS or try to manage everything for him, thinking I could solve it.  I still fall into dysfunctional ways of "helping". But overall, when I really let go and let him deal with his problem, I feel much better.

I'm sorry you are dealing with this, I wouldn't wish it on anyone.

"Lawyer, you misunderstand. The last bit of service we need from you is to get a signed copy of the journal entry. We Will no longer pursue custody from BM, and we will be shutting off SS's cell phone."

That's all that needs said. If you are truly done, then make it clear that you are truly done. You are income to the attorney, so of course they are going to push you to fight. Be abundantly clear that the only "fight" left is the signed form.

Also, if her attorney won't respond, have DH show up to her attorney's office and ask WTH is going on and demand it signed. He's party to that piece of paper, too, and even if he has to pay $100 for the signature, it'd be well worth it.

I've been to court so many times over stupid stuff, one thing I know is that things can and will likely change. The kid is 14, he may decide he wants to live with dad when he's 16 and run away. I'm with the lawyer on this one, don't cut his phone off. That would only cement in his PAS'd mind that dad doesn't love him and mom was right about everything. Even if he isn't responding it's your only line of communication. If dad willingly cuts that communication off then it will be seen as dad giving up.  Mom may have taken the phone away or *accidently* lost it while all of this is going on. It may not be ss's doing at all but yes it should be documented.  Can DH see the phone activity to see if it's being used now? 

Get his attention in a different way. Take your kids on a spectacular vacation and tag ss saying, "wish you were here!" Mean but maybe it will plant a seed that he'd get to do cool things if he spent more time with his father and family.  

You never know what the judge will do. He may order more time with ss due to BM's attitude. She may even be ordered to pay fees since her non communication is costing DH more.  Ask for her to pay up if she doesn't cooperate. 

Regarding the phone situation, DH had a similar issue with SD14.  So he warned BM that SD14's phone service provided by DH would be ending in 3 months, which gave her time to get another plan.  He paid for both SDs new laptops, so this seems like a fair trade. She agreed, then her phone was ended after that 3 months was up.  He has her number and email, I can't believe that the kid's phone you provide is the end-all of communication.  Letters do work too - certified may be a bit much, but you can make copies of letters sent via snail mail and note dates they were mailed.