It seems to me unlikely that she woudl have "come out" at Porsmtouth, except in the sense of visiting friends and if Mrs P wasnt too disorganised, possibly having them to dinner or tea in return.. Balls cost money as well as theatres...in fact they wold probably cost more...

If she'd stayed iwth her own family, she would probably have had just as limited a social life as she did in hte Pre Sir T's return Mansfield days.. and her marriage prospects would be limited to whatever of Will's friends she might have met and who would be willing to marry a girl with no dowry...