I think Peter died and Jane remarried.
FamilySearch has christenings for two children of Peter and Jane: George William (chr. 15 Sep 1861, Salford) and John Joseph (chr. 29 May 1864, Manchester).
Possible death for Peter ASPREY in Manchester, Jun Q 1865.
Jane RIGBY or ASTBURY married Robert DAVIS, Manchester Cathedral, 24 Sep 1866. (Indexed by FreeBMD as ASTBURY)
1871 census
RG10/4020/129/26
9 Sandywell St, SalfordRobert DAVIS Head 48 Iron Moulder b. Preston
Jane DAVIS Wife 34 b. London
George Wm. DAVIS Son 10 Scholar b. Salford
John Joseph DAVIS Son 6 Scholar b. Salford
Jane Margaret DAVIS Dau 4 Scholar b. Salford
Robert DAVIS Son 2 b. Salford
There's nothing obvious for Peter's birth online, is there?

Rambler