I think there would have to be a far greater indicator of a serious mental health problem before she was capable of being committed that what you've put above.
Has there been any violence, self harming, suicide attempts, dangerous behaviour etc...something above and beyond her just making a nuisance of herself?
To be sectioned, she would need to see a doctor or mental health practitioner to get the ball rolling and given the circumstances it doesn't sound like she would do that willingly. She would also need to fit the relevant criteria for being committed and they are quite limited.
Unless she was arrested or similar and the authorities had her assessed it may be that you would have to look at other ways of solving the individual problems such as sorting proper access through the courts (in a contact centre if necessary) for the child, a restraining order to have her kept away from him etc...
Above all he should be careful that if he doesn't take the right course of action eg goes for her to sectioned and she isn't or is and released then he may have an even more ****** off ex to deal with.
Above all, there is a child involved and their welfare and safety should be paramount.