Ron - thank you for the link to the account of the divorce case, which sounds a pretty sad affair in all respects, especially for poor Mrs Shee. The defendant was Captain Pulteney Malcolm RN, the brother of Wellington's close friend John Malcolm, while Pulteney was also well known to Wellington. The connection would not have lessened Major Shee's anger, although it would have been secondary.
Mrs Shee went on to have a son, Benjamin Shee, who was born in 1804 and who appears to have been acknowledged by Pulteney as his - and who was given a junior position on a mission to Persia in c1827 by Pulteney's brother John Malcolm.
I don't know what happened to Mrs Shee.