Your 1850 census for Frederick shows Rebecca born abt 1837 in PA and Samuel born abt 1839 in OH. You said that Frederick and William came to Ohio together, Frederick to Licking Co. and William to Fairfield Co. I have found found the 1850 census in Fairfield Co. for William, which shows his last child in PA born abt 1836 and his first child in Ohio born abt 1838, so that really narrows down the time that they came.
I do believe that Frederick had quite a family with Elizabeth Nagle before Hester and that Jacob and Sabina are probably hers. As to whether her other children went with Frederick to Ohio, at least some of them were under age at the time of the move and probably did, but by 1850 had left the nest, so to speak. As to the "married in Ohio" on one site for Frederick and Eliz., an obvious error.
I firmly believe this Frederick is the son of Heinrich.
Have been searching for your Samuel and not doing very well. By the way, nowhere have I found his wife's name as Lillian. I have always found her listed as Lillie.