Mrs. P. Cullen/Ireland to USA 1836

I am trying to trace my Irish ancestors. My great-great grandmother, Mrs. P. Cullen, came to the USA with her family in 1836. Her husband's name is not known and it is not known if he came to the USA with his family. Mrs. P. Cullen came to the USA with her eldest son, James, age 7; Michael, age 4; and son Peter who was born on the ship crossing the Atlantic Ocean on July 4, 1836. Another relative, Thomas Cullen, age 30, also came with her. We have no record of where the ship docked or where or for how long the family stayed on the east coast before making their way through the Great Lakes to the Milwaukee, Wisconsin area. We do not know if Mrs. P. Cullen was with the family when they left the east coast. We have no record of when or where she died or where she is buried. The first record of her children and Thomas Cullen living in Wisconsin is the marriage certificate of James, dated December 4, 1853. James married Bridget Kelly on that date at Milwaukee, Wisconsin. Some verbal family history suggests the family came from County Tyrone and another time County Cork was mentioned.