Following her arrival in New York in 1913, Bridget Mulvanerty married Maxwell Stadler. The marriage apparently occurred after 12 Sep 1918 (when Maxwell listed his father as his nearest living relative on his registration for the WW I draft), and before 1 Jan 1920 (the date for the 1920 census where Maxwell and Bridget were listed as married).
Sometimes there are romantic stories about where couples met or courted. This isn't one of them. The earliest I've found Maxwell and Bridget together is at the State Hospital for the Insane, Norristown, Pennsylvania. On the plus side, they were not patients -- Maxwell was an attendant and Bridget was a nurse (see the census, lines 38-39). By this time Bridget had changed her first name and was going by Beatrice, too. Maxwell and Beatrice probably left Pennsylvania soon after the 1920 census because their first child, Maxwell Jr., was born in Rhode Island about 1920 and their daughter Beatrice was born about a couple of years later.
Eventually Beatrice married Alfred Joseph Ford, Sr. in Worcester Massachusetts. Beatrice and Maxwell had divorced (her ex-husband continued to be listed in city directories as living in Providence, Rhode Island, from 1923 through at least 1932). I don't know what became of him after 1932.
Maxwell Sr. identified his father as John Stadler in his draft registration. The family can be seen here in the 1910 census (lines 5-9). John's wife in the census is not Maxwell's mother: the marriage is listed as John's second and they've been married 7 years, but Maxwell is 12 years old. Maxwell's biological mother is identified on his birth registration record from 29 Mar 1898 in East Freetown, Massachusetts as Mina.
On all his census records John Stadler is listed as having been born in Germany, and the 1920 census says Baden specifically. One census says he immigrated in 1879, another 1880, and that he was naturalized in 1904. Although I haven't found his initial immigration, I have found a record of what apparently is the family returning from Bremen, Germany 1 April 1902 to the US. This ships passenger list shows Johann Stadler with two kids, Adolf and Max. Johann is the right age to be John Stadler, and also the right occupation (farmer). Max is the right age to be Maxwell, and is noted as a US citizen. They are listed as returning home, so perhaps they had been on a trip to visit relatives in Germany. Alternatively, perhaps the reason I haven't been able to find the family in the 1900 census is because they were in Germany from 1900 until this return: maybe after Mina died Johann returned to Germany with his young sons and only came back to the US in 1902 when Maxwell was no longer an infant. Below is a picture of the ship the family took when returning to the US, the Batavia.