I'm not too familiar with dodging being served papers but this article might be helpful:

https://www.abclegal.com/pro-blog/why-you-shouldnt-avoid-being-served-wi...

her employer? 

My DH dodged Meth Mouth one time.  She kept having some tweaker show up at our house to serve him and we wouldnt answer the door.  Finally she sent the police over and he accepted it.  It's not like she will get in trouble, she just won't have time to respond to what she's being served for and that could lead to the case being dismissed or they could extend it so she has time to respond. 

They can try to dodge subpoenas but obviously there is record of them dodging it and judges do not like it. 
 

If they keep dodging, they stay in contempt of court, then whatever you said they did/owe becomes fact (because they didn't answer subpoenas to prove otherwise). 
 

Make sure you hire a good process server. Mine took pics, license plates, got names of people who answered the door, came at various days/times. 
 

ALL of these minute details can be added up to catch them in lies under oath and shows what type of person they really are (unsavory)
 

*Im not a lawyer but I have dealt with an unsavory bio parent who dodged subpoenas. Each state varies in what exactly they consider "accepting/receiving" subpoenas but I'm sure your processors and lawyers know exactly 

While people dodge subpoenas all the time, I wasn't aware that a business could "deny service." This shows the fatal flaw in your lawyer's ridiculous plan to wait until 10 days before court to serve them. I know you are already stressed, but I think you should prepare yourself for this hearing being rescheduled again because of this issue.

Your lawyer is on the take, or he's buddies with someone.

uncommon tactic in blended family legal action when one side is toxic.

The SpermClan did both. Initially, they would attempt to postpone court hearings at the last minute to put financial strain on my then single teen mom, 3 job working, university student, future DW.  Their goal was to back my FDW into a financial corner and force her to surrender custody of SS. They completely misjudged my SS's mom.  

First FDW identified that the Spermidiot's signature was forged on the suit document.  SpermGrandHag had filed the custody suit without even telling her idiot son. She Had forged the SpermIdiot's name.  FDW then took out supplemental school loans and engaged an attorney.  The first action her attorney initiated was to initiate fraud discussion with the SpermGrandHag's attorney. That attorney resigned. The SpermGrandHag engaged another bottom basement attorney and re-filed, with Spermidiot's legitimate signature the second time. Nearly a year later and three last minute hearing cancelations later, we were able to get a hearing to stick. The Judge tried to back out that time, our attorney was able to prevent it.  The SpermClan dropped the custody element of the case the evening before the hearing and tried to go for joint custody, my DW refused and offered them 9wks of visitation,.  They then proposed 26wks of visitation, DW refused, countered with 9wks. They refused and countered with 15wks, DW refused and countered with 9wks. We ended up in court the next day.

After 8hrs in the court room the final CO was that DW retained full physical and legal custody, CS went from $110/mo to $133/mo and visitation was ordered at 7wks.  

After the Judge issued the CO and as we were all walking out of court, their idiot attorney addressed my DW with "my client has accepted your offer of 9wks of visitation". DW laughed in his face and referenced their idiot attorney back to the Judge's just issues CO of 7wks of vistation. DW's attorney took her by the arm and accelerated the walk out of the court room.

Our attorney's lack of testicular fortitude was part of the reason why we fired her. He goal was making everyone happy, getting agreement between the SpermClan and DW, and to preserve her relationships with the Judge and her peers in the local legal community.  We demanded that she deliver on our expectations.

We went with an absolute shark attorney in our State with zero give a shits about SpermLand courts or SpermLand legal community relationships. They all hated him.

We loved him. A letter from him on his letter head to the SpermClan or their bottom tier idiot attorney of the moment caused absolute panic and returned the results we expected.

After the nearly year long effort to continuously postpone legal hearings after DW had flown she and SS back to SpermLand for last minuted canceled court dates, and 9 years after the eharing, SpermIdiot started his antics to avoid being served for a CS review hearing. He ran from the Constable, refused registered mail service, etc...... 

It cost him/them ultimately. For the most part, we were able to protect SS from them and minimize the majority of their crap over the 16yrs we lived under the CO as SS-30 was growing up.  Ultimately, their crap cost them SS. 

Their loss.  He is an outstanding man of character, a successful adult, and a man of standing in his profession and community.

About 10 years ago, we were living in the Middle East and unbeknownst to us, someone had filed a lawsuit against XH for an incident that occurred when he was an LEO, approximately 7 years prior. It was no secret where we were; a 2 second search on social media would have revealed what country/city we were in and several ways to contact either one of us.

Ultimately it came to light that the process sever had "attempted" to serve XH at several locations over the course of 4-5 weeks or so. Ultimately he ended up at my MIL's and she refused to accept the documents. When she called us to tell us what had happened, it was the first we'd heard of it. We contacted an attorney and that's how we were able to find out what it was about. XH won the lawsuit, by the way, which makes it even funnier in light of how much time and money the plaintiff's attorney spent.

All that to say, first of all my MIL's refusal of service did count as XH being served, legally speaking. And the process server charged the plaintiff's attorney some astronomical amount for the many "failed attempts" to serve. They tried to pass those costs on to us, which is how we found out about the wild goose chase the server had taken himself on. It was absolutely ludicrous for the server or the plaintiff's attorney to assert that they didn't know we were overseas; to me it seemed like a thinly veiled way for the process server to pad his bill. Maybe that's the case with your BM's employer, etc? But in any case I'd expect that the refusal of service won't really matter - it'll count. Or it should! 

It seems like the whole of the local community is on BM's side.  I'm sure she's been bad mouthing your DH for the last 18 years.  If the process servicer is local, they may not be trying to serve her or her employer properly.  Same for your lawyer.  Even if he has seen your side of the story, I've always worried that he was more invested in his standing in the local community then in helping your DH with his case.

Fingers crossed that I'm  catastrophising.

I said it before and I'll say it again. Your lawyer is an idiot. He should have anticipated this. When he told you his "strategic plan" to wait until the last minute, did you object?  They'll eventually be able to serve the subpoenas, but not necessarily in time.  Good luck - I hope it gets done ASAP.

Edited to add:  what exactly is the subpoena to her employer? Is it a subpoena for business records or a subpoena for someone to testify as to whether BM works there, and if so is it for a particular person? If business records, you're probably screwed - a google search turns up a Kansas statute that requires notice, 14 days to object, and more for non-party business records. If you're looking for a particular individual to testify, maybe that person isn't there and other employees won't accept service on his behalf? I'm far from a lawyer, though. I would make your lawyer explain it all and tell you what his Plan B is.