Hello Jeanne! Well, I can at least give you the basic information about Texas records. Texas did not require death or birth certificates until 1903. Even then, the law was not strictly enforced until the 1910's. So it is doubtful there is a civil death or birth registration for Albertina or her (possible) child. That being said, there's always a chance, so you might write to the Galveston County clerk just to make sure there is no record. You can always get lucky! (But be prepared, it isn't very likely).
There may be some information from other sources, though. What religion were they? Catholic? Lutheran? Both of those keep great records, so there might be something available.
There may also be funeral home records. Do you know where in Galveston Co. they lived? There are several cities in Galveston Co. (Galveston and Texas City to name two). The local library may have some info on funeral home records.
As to Hilder, have you found him in the 1880 or 1900 census? Do you have a date of birth? A date of immigration? The Navy reference is very interesting. Did you take the reference to mean he was in the US Navy? Was he ever naturalized? I'm not sure about a naval base in Galveston...I know there is one in Corpus Christi (Nueces Co), but don't know how long it has been there.
Be aware that a MAJOR hurricane hit Galveston (the city) in 1900. The whole island was under feet of water. That may have had some impact on the records available.
Couple of suggestions. First, you should post this on the Galveston Board if you haven't already. Then you might also go to the Random Acts of Genealogical Kindness http://www.raogk.org/http://www.raogk.org/ and see if there is a Galveston Co. volunteer. They might be able to find something in Galveston Co. Finally, if you have some additional info about Hilder and Albertina, (birth, immigration, city, any Texas records you found, location of death for Hilder) post here again and maybe we can find something.