I suggest you have an appointment with the doctor and review details on how it is working now, what's not working well, and how using a pump and cgm would improve things for your mom.
If insurance is going to be involved with covering the pump and supplies, the doctors (or their staff), do spend considerable time working with the pump companies and insurance companies to get approvals. Often representatives from the pump company (Medtronic, Animas, Tandem, etc), can also do a lot of the legwork.
So if you have a specific company in mind, you may want to start with contacting them, and your doctor might be willing once they are providing much of the paperwork.
But ultimately a physician needs to provide the Rx, so you may need to find a new physician that would support it.