The leaves look and sound like it might be a Rugosa. Try a search on Rugosa on HelpMeFind or go to VintageGardens.com or some of the other OGR sellers and look at their descriptions and photos of rugosas and see if it matches. It's a start.

Here is a link that might be useful: Vintage Garden's Rugosa List

You have supplied a classic description of a rugosa. Here's a link to photos at helpmefind; most of the photos are good, except one showing a brick-red flower (must have been a trick of the light), and another showing a semi-double flower (they're usually single flowers). Magenta is a hard color to capture on film.

Here is a link that may be useful: Rugosa rubra

flowersandthings, if your great-grandmother's rose is a rugosa, it should be easy to propagate. Most rugosas have a tendency to send out rooted "suckers" that can be cut from the mother plant. The webpage I've linked to below shows what to look for, althought the plant illustrated is not a rose.

Here is a link that might be useful: Propagating from suckers

Yes, rugosas are easy to propagate. As a guarantee, you can collect hips and store them in the fridge. Jan 1st, open the hips and take out the seeds. Put them in a small ziploc bag with some moist potting medium and store in the fridge for three months. April 1st you can put them outside. Since you live north of me, you might want to time putting the plants out later than April 1st. The main thing is to give the seeds 3 months of cold moist stratification. Rugosas are easy as pie to grow from seed. Of course, if you can dig up some suckers or get some pieces to root, you won't even need the seed!