I think the 1841 Lowes family in Heworth is the right one, just mistakenly put down as all born Durham. Ages are a little out but not unusual.
Esther Lowes is living with a Taylor family in Tanfield in 1851. This appears to be her mothers family, as from the GRO birth index for Esther and John George, their mother Eleanor Lowes maiden name was Taylor.
In 1851 Eleanor is down as born Newburn, in 1861 born Denton Burn, so this is probably her baptism.
1 Sep 1816, Newburn. Eleanor Taylor, daughter of Samuel and Mary Taylor, of Denton Burn. Father a Coal Miner.
The Taylor family in 1851 at Shield Row, Tanfield :
Mary Taylor, Head, 73, Widow of Coal Miner, b. Chester le Street.
William ", son, unm, 48, Coal Miner, b. Northumberland St. John.
Edward ", son unm, 27, Coal Miner, b. Gosforth,
Esther Lowes, Visitor, 11, b. Heworth.
So these are probably William and Edwards baptisms :
27 Dec 1823, Newcastle St. Nicholas. Edward Taylor, son of Samuel and Mary Taylor, of Kenton. Father a Collier.
20 Jul 1806, Newcastle St. John. William Taylor, born 28 Mar 1806, 3rd son of Samuel Taylor, Pitman, native of Lamesley, by his wife Mary, daughter of William Robson, Native of Chester le Street.
Alan.