Darn. Just lost my whole posting somehow so I'll be brief.
Your Philip Dux may well be connected to my Anna Dux, born ca. 1840 in either Hessen or Baden, who emigrated to NYCsometime before 1860. She married Joseph Becker, born 1829 in (probably) Baden, who emigrated in 1854. They eventually owned a saloon on West 39th Street.
Children included Catherine/Katie (b. ca. 1858, m'd Jacob Zwicker, and moved to Dumont, NJ); Joseph (b. 1860); Christel/Christie (b. 1866, m'd Elizabeth/Lizzie); Sophie (b. 1869, m'd William Boyle, a police detective, and eventually, I think, moved to Flushing); Kasper (b. 1872); and August (b. 1885, m'd Kate, was running the saloon in 1910 and thereafter moved to Fort Lee, NJ).