This is an interesting tale, and very very sad, it seems that Joe and Sydney may have known each other for quite a while. They lived in the same area.
As poor Sydney was taken to Wrexham then her death would be registered there. Joe was in Hope, and would have been registered Chester.
Deaths Sep 1901 .
Guest Joe 34 Chester 8a 273
Jones Sidney 40 Wrexham 11b 165

I wonder if this is the lady, there are not many Sydney`s around.
1901
RG13; Piece: 3379; Folio: 178; Page: 17
Bryn Golau, Cymmau.
Sydney Jones F Single 38 head. farmer, own account b Liverpool
Maggie F Jones dau Single 18 dressmaker own acc at home b Hope.
I think this confirms it

1891 RG12; Piece: 2870; Folio 103; Page 15;
Cae Clogyn Farm .
Sarah Jones 68 head Single, b Hope
Sydney Jones 28 neice Single ,general dom b Liverpool.
Margaret Florence Jones 8 neice b Hope
Joseph Guest 24 Single, servant b Hope
Thomas Edwd Whitley 14 Single, servant b Hope
Edwin Jones 40 Single, servant b Hope
Who was Maggie`s Daddy.

1881 RG11; Piece: 3566; Folio: 82; Page: 15
Cae Clogyn farm
William Jones 92 Head Widower Farmer of 52 acres b Hope
Sarah Jones 60 dau unm housekeeper b Hope
William Jones 50 son Unm labourer b Hope
Sydney Jones 21 Gr Dau, Unm dairy maid b Hope
Jesse Cox 16 male farm servant b Buckely.
1881 RG11; Piece: 3566; Folio: 50; Page: 41;
Caeau , Caergwrle
Joseph Guest 58 head labourere b Hope
Elizabeth Guest 32 wife b Llanarmon Denbs
Joe Guest 14 son b Hope
Rachel Guest 8 dau b Hope
1871 RG10; Piece: 3737; Folio: 50; Page: 12;
Cae Clogyn
William Jones 82 Head farmer b Hope
Margaret Jones 78 wife b "
Sarah Jones 50 dau Un b "
William Jones 40 son unm farmer b "
Robert Rowland 17 unm servany b Liverpool
Sidney Jones 11 gr dau b Liverpool.
1871 RG10; Piece: 3737; Folio: 21; Page: 38
Brickfield Caergwrle
Joseph Guest 37 widower farm lab b Hope
Mary Guest 14 dau b "
Catherine Guest 8 dau b "
Ellen Guest 6 dau b "
Joseph Guest 4 son b "
Just a "maybe "
1861 RG9; Piece: 2670; Folio: 10; Page: 14
10 Pall Mall Ct, St Pauls, Liverpool
Hy Jones 29 porter b Wales
Ann Jones 25 wife b Wales
Hugh Jones 3 son B Liverpool
Sidney A Jones 2 dau b "
Wm Hy Jones 4 Mo son b "