Ok, I have a somewhat similar set-up, except in that I am not attempting to heat any room other than the room the stove's in. In my case, I built an attached greenhouse with French doors into the kitchen. The walls are field stone up half way, then cedar shiplap above that. All walls insulated with fiberglass. The glass is double-paned. And I've had this set up since maybe the late-80s, so we have a long-experience with it.
The stove I have out there is a good heater. And when the fire goes out, the room begins to cool and in a couple hours can be chilly. The big, therm-paned windows [actually replacement patio-glass-door units, ten of them] transfer heat efficiently...to the outdoors. The stone walls and tile floor no doubt warm up some, but the re-radiation of heat from them is pretty much negligible in a human-comfort sense.
In short, I would be pretty unsuccessful trying to get much heat from that room into my main house. [Which has two other wood stoves and doesn't need the greenhouse heat anyway.]
All this to say I believe from my experience that you are basically able to provide heat to that one room with perhaps a little bit available to the house if you ran some fans to circulate air, but not very much net increase in house temp. Even if you were to invest in purchasing or making some good window coverings, you still would not have a great heat source for the house. Better, of course, but not great. Or, I don't think so.
Best bet is to relocate the stove to indoors if possible. A hassle, some cost, but you'd have heat in the living space.
One other thing: during the day, if it's sunny, my greenhouse can really heat up. No need for a stove then and I don't run it. I have a fan blowing air into my kitchen from there, and another fan blowing air back into the greenhouse, so a circulation going. This can heat up our house to the point we don't want any more heat, and we let the house stoves' fires go out. Then, at sundown, those fans need to be OFF. I have them on a thermostat, so no problem. In your room, I don't know whether you get any solar gain, as in my case there are glass panels overhead [it being a greenhouse].
As to your question whether a pane of glass is going to keep heat inside better than thin plastic sheeting, a little bit, emphasis on "little." Even double-paned windows let a lot of heat through them, not as much as single pane, but plenty.