It's important to remember that what matters for ESA is what she can do, not what her diagnosis is.
So when you approach her doctor, you may find it helpful to refer your doctor to what you consider to be the relevant ESA descriptors and ask him whether, having regard to what he knows of her, he feels there is anything helpful that he could put in a medical report.
It may be that he will be prepared to provide her with a medical report for her to send in with her ESA50, but you should be prepared for the likelihood that he may prefer to wait for the DWP to send him a form.
Either way, if your wife has discussed it with him, drawing his attention to the relevant descriptors and asking his opinion, you will have an idea of whether his report will be helpful.