] Does anyone have any insight into the meaning of that bolded phrase? Would they be pinning up each other’s train for dancing whilst in the ballroom, just to keep it out of the way,

Actually this is quite sensible. It is more mysterious, what a pin was doing in Mrs Allens sleeve, except tearing a hole in it and making a distraction in Catherine's and Henry's talk. My imagination fails. Any alterations to clothes would be done before a ball in a dressing-room, and probably with needle and thread. Perhaps it is a euphemism for the seat of Mrs Allen's dress, for she, too, pinned her train - to move in a crowd. Any ideas?