You would need to purchase private insurance coverage. Sponsored immigrants are not eligible for means tested benefits, which can include most medicare services.
Here's a link to the
I-864 Affidvit of Support for sponsors. You would need to prove enough income to support your family members in your own household (if you're married with kids), plus your mother. And here is the
Poverty Guidelines.
You would send the petition to the Vermont service centre address (I think, don't quote me on that, read the instructions on the form), and I believe you would request that the immigrant visa be issued in Montreal. Your mother cannot stay in the US during the processing, as adjustment of status is not available to family members other than spouses.
You may want to consult with an immigration lawyer for your options and current laws regarding sponsoring parents. I'm not a lawyer, I'm just an immgrant married to an American.