] I rather think that the poor other son was not connected with fine clothes during the course of the conversation and so Mrs. Allan does not remember him at all!

I conclude that he must not have been mentioned at all, at least not in conjunction with his profession. I find it hard to believe that Mrs. Allen would have forgotten a red coat. ;-)

] Regardless of the details of the scene, why does Henry think to include Captain Frederick in his little made-up scenario in the first place?

I don't know about what Henry is thinking, but I suspect that JA put this mention of Capt. Tilney in here merely to introduce him to our notice. Perhaps he will figure in the story somehow later on and this is her sly way of working him in. ;-) Yes, I know it's a boring, unromantic explanation, but there it is. ;-)