For all the kannaim here, there is a tshuva of Reb Moshe to a Rabbi Yalow in Syracuse, regarding a giyores whose mother was ill, and wanted to see her children and grandchildren. After some shakla vtarya on this Rov’s suggested heter, Reb Moshe says there is another much more basic reason to be matir. People will say that dinei torah are not b’yosher. How could it be that somebody who converted to a higher kedusha ends up giving her mother less kovod than when she was non-Jewish? So from menschlachkeit considerations, Reb Moshe says she should visit her mother.
(The reason in general why too much visiting is discouraged, is so that the giyores should be able to build her new life, and not fall back into her old patterns, and end up abandoning her new-found religion. However, that does not mean one cuts off her family, and shows disrespect or cruelty.)