How can i convince my mom to have surgery on her clogged arteries in her neck?

Don't. : Don't. The way your mom needs to come to this decision is on her own. You can help by finding a good vascular surgeon who can sit down with her and explain the reasoning behind surgery. In many circumstances surgery offers a lower risk of future stroke. This can be a very complex decision and she'll need to have a detailed discussion of the risk, benefits, and alternatives of surgery.

Convince Mom: Tell her the procedures to fix carotid lesions tend to be very effective, result in usually only an overnight stay, and have very low complication rates when completed by a well trained physician.