When you are playing a COTM the R&R mods and rules are not involved at all. You are playing standard, out of the box, Conquests, with the barbs fixed if you apply that patch.
I don't know R&R, but I've had a quick look at Double your Pleasure which was its predecessor. DyP and standard Civ are two different games, with different techniques needed to do well. You can't expect to use the same strategies successfully for both. I expect R&R and standard Conquests are equivalently different.
Whether it's confusing or not to try to play both depends on whether you can separate them in your mind and treat them as different games.
Re. your game, you won, didn't you? What's the problem? If you choose a non-military victory condition have to decide whether to sacrifice military strength in order to maximise research. If you do you may get kicked around a bit. Did you build mainly defensive units? If so you might want to try building more offensive units and using "active defence" - kill before you are killed. The AI respects offensive strength more than defensive, and is less likely to attack you in the first place if you have more offensive units.
Try a C/GOTM and see how you get on. Submit your games. Compare your approach with that of the leading players and you'll improve your Conquests play. Will that improvement rub off on your R&R play? I've no idea!