Hiya
I think then that the birth certificate you have is for the wrong Price Evans and his father was RICHARD EVANS.
I had another look at the the baptism entry and its Richard and ELIZA (not Elizabeth), sorry it was late when I posted last.
There is also a baptism for
Mary EVANS 08 February 1850 Father: Richard Occupation: Farmer Mother: Eliza Abode: Perthybu
I think I have the family on the 1851 Wales census living in Broncoed (a part of Mold as you go out towards Buckley)
Ref: HO107/2501 Folio 393 Page 1
Richard EVANS, Head, Mar, 31, Farmer b. Treuyddn
Eliza EVANS, Wife, Mar, 28 b. Nercwys
William EVANS, Son, 4 b. Mold
John EVANS, Son, 3 b. Mold
Mary EVANS, Dau, 1 b. Mold
Mary Jones, Serv, 18, House Servant b.Mold
But of course your Price wouldn't be on it as he'd not have been born yet! There is another possibility (although admittidly a long-shot as it would have had to have been a later registration)
Edward Price Evans 1852 Q3 Holywell,11b 275
northwalesbmd show it as being a Mold birth and he may have dropped the Edward; apparently it was not uncommon for this to happen.
Northwalesbmd has a marriage of
Richard EVANS and Eliza TYLER occring in 1846 Nercwys
GRO is 1846 Q2 Holywell,27 413
Is this them in 1881 at 17 Alun Bank, Mold Price being a coal miner? Ref: RG11/5507 Folio 51 Page 46
and again in 1891 living on Rhydygaled Road with their four children? Ref: RG12/4609 Folio 116 Page 1
And there is a death entry for Price Evans that would seem to fit age wise
1897 Q4 Holywell,11b 167 Aged 45
Apologies if you have that already!
There is another Price Evans born 1851 Mold married to an Elizabeth on the 1901 Wales Census; I think this is the son of Robert and Ellen / Eleanor Evans thats been confusing things.
I hope this has been of some use, and hasn't added to the confusion.