Wow, yeah, not good sidewalks for running on. Plus, asphalt is a bit easier on the knees.
I don’t think it’s rude; just be alert, run against traffic, etc. as you’ve already mentioned you are aware of and will do.
Some people will be jerks and won’t share the road, but that’s just the way they are. Be ready for them.
We don’t have sidewalks out here, just very narrow gravel shoulders that aren’t very well groomed --cow hooves are hard on them, since cows just can’t be bothered to stay on the flattop and will wear down the sides, plus chop up the top anyway. So we don’t have any choice but to run on the road and still people will do various things to (apparently) communicate their displeasure with our enjoyment of the outdoors: speeding up to 70ish (on a road that isn’t posted, but should be 25), not moving over at all (which is just a courtesy, really, it just lets me know you see me and don’t intend to run me down just yet), when it’s a car coming from behind, I’ve had people come across the center line to get closer to me (I’m never sure if this is bad driving–steering where they’re looking–or assholery) and when the weather has been bad, I’ve been drenched head-to-toe in slush and cinders by people combining the close and too fast aspects with driving through the closest puddle even if there’s plenty of room and a high cleared section of the lane.
I still always smile, try to make eye contact and wave. After all, this is a rural area and these people are likely my neighbors, even if they’re not acting very neighborly.
I try to run at times of day where the sun won’t make seeing the driver inside the vehicle difficult, although some people’s windows are so dirty time of day doesn’t matter.
I do the courtesy wave thing when I hear a car coming up from behind and I try to have my head turned enough to both watch where I’m going and watch where the car is going, so I can jump down the soft gravel shoulders if I have to, figuring if they want to run over me/bump me with the car, I’m taking them with me. Only problem with this plan is there won’t be much time to make those assessments, and at the bottom of the shoulders are barb wire fences. Still, I’d rather look like an idiot (who’s up-to-date on her tetanus) than hit by a car/end up like Lance Cpl. Suzanne Marie Collins (when I initially read about the case it was said he used the car to incapacitate her and unfortunately her death has really stuck in my mind).
The nice thing about running in the road is also the extra space from unsecured dogs. I haven’t yet run into a dog that really means harm and thus hasn’t been stopped in their tracks by a firm “NO!” and pointing The Stern Finger of Doom and “GO HOME!” but those extra feet of distance from the houses have given me the time and space to stop moving and shout to stop them before they’re on me/too close for their arousal levels. The dogs that don’t bark are the worst and get the closest. Of course, where you’re running, you’ll probably need to be extra alert since a dog could pop out from between parked cars at you and send you into a car’s path if you startle. A little can of pepper spray can be a nice thing to have as peace of mind against aggressive dogs or people. But you should be fine. Running outside is so much better than running on a dreadmill that it is well worth the risks. And when you have more time to run, definitely hit the trail, it is so nice to just focus on the footing, the scenery, your breathing…no worries about cars…just mountain bikers and horses. 