He should not reply at all and ignore any communication not directly necessary and involving the kids. That's what i do and it seems to work. 

Any time BM has turbulence or is single she gets real effing chatty. "I cannot Satan, stand down", is what I would tell her but am no contact with her myself. I let my husband  know that it was unacceptable  if it's not about the kids it doesn't need to happen. Period... 

I think he started saying something probably, probably that I needed to be nice for the kids or something but I cut him off. I asked him why he was good enough to support her now when he wasn't good enough when they were married... she had beeeeeeeest frands (men she was sleeping with), that she needed their constant validation. He dropped it and now ignores her when it's not about the kids. 
 

I had to raise a stink to get the point across. I hope it's out of respect for our relationship but if it has a little to do with fear of my reaction, I'm okay with it. 

BM has done this before, except it was his birthday and what would have been their 15 year anniversary.

Yep, you read that right. The woman who divorced DH in a fairly heinous way had the nerve to text him on his birthday, which also happens to have been their anniversary, to wish him a happy birthday and say "gosh, had we stayed married, we would be celebrating 15 years this year". And no, I don't think she was trying to twist a knife in his back. I think she thought she was being genuinely sweet/sharing a sweet sentiment.

It irked DH. It pissed me off. This was a few years ago at this point, so I don't remember 100% what his response was. I actually think she said it during a phone call, so I think he ended the call pretty quickly after that.

If she messages him any more, he doesn't tell me about it, which is fine. She tends to be a roller coaster of emotions, so her behavior is never consistent except that it's always inconsistent. 

I guess it depends on the nature of their split.. if they are "hollyweird" intentional uncoupling... then I guess they may have these niceties flowing.. but for the majority of the world, such pleaseantries are not really necessary nor appropriate.

If I were your DH I would have deleted and ignored the texts.  You can't control what the other person does, but you can control your response.  When the texts went unanswered perhaps she would get the hint and lay off the best wishes.. if she followed up with a "did you get that text" he could respond that "yes, I got them but to be honest, I really want to limit our communications to things that relate to the children, so I did not respond".

I think your DH handled it perfectly. Thanks. No reason to make it clear well wishes aren't wanted. I mean, why does anyone care if someone wishes them or their spouse happy birthday?

Goodness gracious, I honestly do not know how any of yous can stand having BM know your private personal cell phone number/s.

Dh and I had cells for years and years. We never EVER told her the numbers. The Judge didnt order it either.

IF, gosh forbid there was a awful, terrible emergency she could call the land line OR call the police who will call our police to knock on our door. OR she can call her free lawyer who will call OUR lawyer.