Karisue: Have a book "A Courageous People from the Dolomites" that was given to my mother-written by Bonifacio Bolognani. In it it has a list of people who immigrated to the U.S. I check it out to see if any of the above names you had were listed - this is what I came across.
On the name: MARINELLI: From Vigo Di Anaunia - VITTORIO who settled in NYC; From Casez - Val Di Non - LODOVICO and CESARE they both settled in L.A. Calif.
On the name: PELLEGRINI: From Varone - riva Del Garda LUIGI who settled in Mt. Carmel, Pa.; From Salter - Val Di Non AURELIO Who settled in Kemmerer, Wyo; From Malgolo Val Di Sol ALBINO who settled in Chicago, Ill; From Damel Val Di Non these 3 people: ALBERTO who settled San Louis, Mo; GIUSEPPE sho settled San Louis, Mo; and GIOVANNI who settled in Telluride, Colorado. Have no dates when they came over just what is listed above. Hope this will be helpful somehow.
According to my mother: Val Di Non means valley of the grandparents. There are 10 valleys in the Province of Trent: Adige Valley, Vallagarina, Upper Valsugana, Val Di Non, Val Di Sole, Sarca Valley, Giudicarie Valleys, Lower Valsugana, Fiemme Fassa Valleys, and last Valleys of Primiero
The town that my grandparents came from is Segno.
Hope this is of some help. Good luck in finding more of your family.