Getting Everyone Involved

Over shabbos I heard a beautiful pshat that I just felt that I had to share.
In last week's parsha, Parshas Vayeira, we see the hachnosas orchim of both Avraham and Lot. If one looks we can see many similarities between the two. They both bow to their guests, invite them to their homes and offer them food and water to wash their feet. In fact, Lot invites them to spend the night which Avraham doesn't (probably because they arrived to Avraham at midday and to Lot later in the evening). Obviously Lot learned how to be machnis orchim from all the time he spent with Avraham.
Harav Samson Raphael Hirsch points out a very interesting difference between the two. By Avraham it says, that he ran to Sarah and told her that they had guests and that she should bake cakes. Then he got a calf and gave it to Yishmael to prepare. Whereas by Lot, the passuk basically tells us that he did it all himself.
Obviously when one acts like Avraham involving the entire family, the trait is perpetuated, as the gemara tells us that one of the primary traits of klal yisrael is gomlei chasadim. Whereas if one does it on his own without involving his family, the trait ends with him. As we see with Moav (descendants of Lot) that the primary reason Klal Yisrael was told to eradicate them was not because they hired Bilam, but "Al asher lo kidu eschem balechem uvamayim", because they were not gomlei chesed to us when we left miztrayim.
The (former) Belzer Rebbe learns this same lesson out of a passuk in Haazinu, "Hanistaros, LaHashem Elokainu, Vehaniglos Lanu Ulvanainu Ad Olam", pashut pshat is that Hashem knows all secrets, but public things are known to all. The Rebbe explained it though as follows, acts that are done privately stay between that man and Hashem, however acts that are done publicly, i.e. involving the family, remain with us and our children until the end of time.