Is there any other communication she can use? How old is this child? Can his father's number be provided to her instead? How often is this kid in your care? Etc. You have a right to boundaries. If you don't feel that she would use it properly, and she can communicate with her son via his father, then that's what her ex should give her. You did not say she wanted it for an emergency. You said she wanted it "to keep in contact with their son". So why YOU and not DH?
I have had very little communication with the sks' BM directly and she was not the type of person I wanted a relationship with. We kept a land line and if she could not reach the kids on their own phones, she used the house line like everyone else. The kids also called her on that line if they were not able to use another phone. I did occasionally receive a call from the kids via their mom's phone so I had the number (and she had mine) but she did not call me directly, nor did I call her. I only kept the number in case of an emergency. Keeping in contact did not involve me.
If you think she would call or text or involve you in things that are really to be handled by your husband, then I would proceed very very cautiously. They're going through a contentious time and you and your children do not need to be dragged into it. Even if you only see her at drop offs or pickups, practice saying, "That is between you and DH" if she tries to reel you in. I firmly disagree with the person who thinks that you should allow her to dump on you about your husband. She needs to find a friend to do that, not his wife.
RE: weekend visitation or such, that is between the parents. Your DH should talk to you to make sure you don't have a conflict, but it's not your job to arrange his time with his child with his ex. They need to communicate and if they can't talk nicely on the phone, that's what email is for. I helped raise my SD from the time she was 6 and never had a need for weekly communication with her mother.
ETA: if she knows that a legal battle is coming, I find her timing suspicious. So keep your eyes peeled and very firm boundaries!