First of all, Fanny does not hold any real importance to the people in MP (with the exception of Edmund). They use her as an unpaid servant, but being a Dependant is different from being a sibling and a daughter.

and when to these sorrows was added the idea of the brothers and sisters among whom she had always been important as playfellow, instructress, and nurse, the despondence that sunk her little heart was severe. Chap.2

Second, she especially misses the day-to-day presence of her beloved brother, William. She gets to meet him twice in all the years of separation. She would have the chance to meet him more frequently if she was in Portsmouth, since his ship would be moored there. and as his parents, from living on the spot, must already have seen him, and be seeing him perhaps daily Chap. 24

We used to jump about together many a time, did not we? when the hand–organ was in the street? Chap. 25

This presents such a sweet and innocent picture of their childhood, and indicates a freedom of spirit that has been sorely lacking in Mansfield Park.