I checked the indexes for your Burie Smith and did not find him.But when I looked at the actual records, think I DO see him:
As indexed: 1910: Brantley/Opp Rd, Copperas Head, Covington, Alabama, p10b John W Smith45m Cusie B Smith27f Hester G Smith4f Bessie Smith2m Tendie V Smith1-3/12f
My reading (both parents had been previously married): 1910: Brantley/Opp Rd, Copperas Head, Covington, Alabama, p10b John W Smith45md2-2yrALALGA Carlie? Smith27md2-2yr3/3ALALAL Hester G Smith4 Burie Smith2 Trudie V Smith1-3/12
As indexed: 1920: Pct. 1, Oldtown, Coffee, Alabama, p2b John W Smith 56 Jenie B Smith 36 Hester Smith 15 Berry Smith 12 Trudy Smith 11 Lothar Smith 7 Preston Smith 5 Odus Smith 4 6/12 Olien Smith 2 1/12
My reading: 1920: Pct. 1, Oldtown, Coffee, Alabama, p2b John W Smith56mALALGA Venie B Smith36f Hester Smith15f Bury Smith12 m Trudy Smith11f Luthar Smith7m Preston Smith5m Odus Smith4-6/12m Olien Smith2-1/12f
I can email you these two census pages if you cannot view them at ancestry.Let me know?