I found one Limpier on the TX Dth Idx 1890-1976. Could this be a son of your Mary? From census I see he names a daughter Cora, too.
TX Dth Idx 1890-1976:
Name: Edward Limpier Death date: 13 Feb 1949 Death place: Fredonia, Mason, Texas Gender: Male Race or color (on document): White Age at death: 83 years 5 months 12 days Estimated birth year: Birth date: 31 Aug 1865 Birth place: Mason County, Texas Marital status: Married Spouse name: Father name: Father birth place: Mother name: Mother birth place: X Occupation: Farmer Residence: Fredonia, Mason, Texas Cemetery name: Hext Cemetery Burial place: Hext, Texas Burial date: 14 Feb 1949 Additional relatives: Film number: 2223285 Digital GS number: 4031778 Image number: 1342 Reference number: cn 20068 Collection: Texas Deaths, 1890-1976 Informant: Eugene Limpier
On the later TX Dth Idx and SSDI, Eugene Anderson Limpier is the only Limpier listed. Sounds like Mary's name was changed at least a little along the way, or her brother would show up someplace.
I would try and track down descendents, if any, of Eugene, see if they know anything about the family line.
I understand there are early ship passenger records in Galveston, maybe someone could check on that for you. Probably not a good time right now to get some research help in Galveston, but try later when things are put back together from the flooding etc.
Have you tried Steve Morse's One Step sites?Some are for a fee, but there are free ones. The free Galveston one is real slow this morning, so you might like to try it and the one on New York for your family name.http://stevemorse.org/http://stevemorse.org/