We know that they were married in Dublin in 1873. Was there an Irish census in 1871? Have you found the family in later census records, other than 1911? I seem to remember from my own Irish family research that early census records were destroyed in a fire.
Were her parents' names, William and Jane, from the marriage certificate? Marriage records in England at the same time include the names of the fathers of bride and groom and whether they are still living, and also include birth place for the bride and groom. What information is on Edward and Maria's certificate? If you have a civil certificate, might there be a church record with more information?
If you do have information that Maria's father's name was William, have you checked for a possible match in the Ireland Civil Registration Index? There are two good possibilities in Dublin South deaths: born 1826, died 1886; and born 1812, died 1887. Jane Mallins is less common, with only one woman in the entire Irish Civil Registration Index, 1845-1958: born 1826, died 1888 Dublin South.
I think at this point your best bet is to try to find Maria's family in the UK. Are there city directories for Dublin around 1873?
--- added later:
You have a photo of Maria Mallins Howley, "late 1880's, Ireland"; I don't see the "Indian" features you talk of. Her hair is light, her eyes are light, eyebrows are light. Her eyelids slant to the outer corners, but my German-born husband's eyes do that, too. That single early photo seems to refute the "Indian" story. Especially any of the features of Native Americans other than perhaps the plains Indians who many people refer to as having "typical" features.
I should have checked your family tree for the marrige certificate. We see Maria's occupation is weaver, as is her father's, William. With the address, you can search for Maria's other family members. Hopefully you could find a descendant with a family tree, or perhaps an obit which mentions travel to the U.S.
You have the name of the Catholic church they were married in: I think it would be prudent to check the birth records of that parish for Maria's birth, if all else fails to produce a U.S. birth record.
Why do some of the Mallins / Howley family trees show Maria's parents' birth as Spain? Some also state that at least one of her children was born in Spain?