Like the other person said she sounds like she is harassing y'all and you can report her for that. Get copies of phone records, write down the times she calls drunk, etc. She doesn't need his cell number, that is ridiculous.
Oh and there are web sites for divorced parents that has the childs info and dr visits, activites, report cards, you can corrispond and lots of other things as well as a place to keep court documents.
legally the only phone number she should have is his home number but also legally he is the one that needs to talk with her no matter what she says! He is the parent and the courts will not see that as a good thing if he does not talk with her.
Now if she causes problems he can limit the calls to emergencies or none emergency calls set at a certain time. But he can say if you are going to talk about other things I will have to hang up. He shoudl not even resonf to other things and just say is there saomething you need concerning ****** (the babies name)
If she will not stop then he neds to record it and he can get her for telephone harrasment and show the court he is willing to discuss the child just not other things. I have seen children taken away from one parent and given to another becasue of imature behavior like that.
But really I can not express enough that he needs to be the one to talk. ALso some courts will tell parents to talk via email so there is written words and can be taken to court, except for emergency calls.