They are on the 1900 census for Dallas Co, TX. By 1920 Bridget no longer with them. This gives you the spelling of Havey. Plus given name of Bridget's husband.
TX Dth Idx thru 1976:
Name: Mary Havey Madigan Death Date: 18 Nov 1948 Death Place: Dallas, Dallas, Texas Gender: Female Race: White Death Age: 80 years 1 day Estimated Birth Date: Birth Date: 17 Nov 1868 Birthplace: St. Louis, Mo. Marital Status: Widowed Spouse's Name: Father's Name: Patrick Havey Father's Birthplace: Ireland Mother's Name: Bridget Lawless Mother's Birthplace: Ireland Occupation: Housekeeper Place of Residence: Dallas, Dallas, Tex. Cemetery: Calvary Hill Cemetery Burial Place: Dallas, Texas Burial Date: 20 Nov 1948 Additional Relatives: X Film Number: 2223076 Digital Film Number: 4031449 Image Number: 123 Reference Number: cn46921
Go to Find a Grave site -- http://www.findagrave.com/http://www.findagrave.com/ -- I entered Mary Madigan, selected state of Texas and selected county of Dallas. You will see the double headstone for Mary and her husband John.
This is interesting, maybe Bridget's husband was John, not Patrick. DCs are notorious for having errors.
1860 census St Louis, MO (location listed for birth of Mary)
Harvey[sic], John, 31, b Ire " Bridget, 30, b Ire " Edward, 2, b MO Lawless, Bridget, 47, b Ire (probably your Bridget's mother) " Patrick, 29, b Ire " James, 26, b Ire
1880 census St Louis, MO:
Category: Name;Relationship to head of househod; Marital Status; Gender; Race; Age; Birthplace; Occupation; Father's Birthplace; Mother's Birthplace.
Bridget HAVY[sic]SelfWFemaleW50IRELANDKeeping HouseIREL.IREL. Edward HAVYSonSMaleW21MO.TeamsterIREL.IREL. John HAVYSonSMaleW17MO.TeamsterIREL.IREL. Mary HAVYDauSFemaleW15MO.Dress MakerIREL.IREL. James HAVYSonSMaleW8MO.At SchoolIREL.IREL.
The son Edward matches little Edward on the 1860 census.