Just found this 1880 Census which seems to be parents of May.

1880 Census in Elizabeth, Union Co NJ
Centre St.
William REYNOLDS age 29 NY PA PA printer
Josephine wife age 23 keeping house NJ Russia Sch???(spelling is bad and could be Czechoslovakia?)
Elzada dau age 3 NJ NY NJ
William H age 1 NJ NY NJ

City Directory for Elizabeth NJ:
Name: William H. Reynolds
Location 2: 710 First avenue
Occupation: deputy revenue collector
Year: 1886, 1887
City: Elizabeth
State: NJ

Name: Wm. H. Reynolds
Location 2: 29 Seventh
Occupation: collector
Year: 1888, 1889
City: Elizabeth
State: NJ

Name: William H. Reynolds
Location 2: 27 Seventh
Occupation: collector
Year: 1890, 1891
City: Elizabeth
State: NJ

Wife Josephine must have died bef 1900 Census and after May was born in 1890. Could it have been from complications of childbirth? She did have dau Josephine born in 1889.

Wasn't the dau Josephine residing with William and May HILGENDORFF in a later census, and was not married then?

Maybe you can find a death date for the mother Josephine in Union Co?

I think this is the son William shown in 1880 Census, married and with a dau named Josephine too:

1900 Census, Elizabeth Union Co NJ
530 Westfield Ave
William S Hedley 52 8/1847 m29yrs Wales Wales Wales emig 1871, 29 yrs in US, nat, mason, owns home
Annie Hedley 53 3/1847 Wales Wales Wales m29yrs, 10 children, 8 living, emig 1871, 29 yrs in US
Jennet F Hedley 21 12/1878 NJ Wales Wales clerk dry goods
Nellie B Hedley 19 1/1880 NJ Wales Wales clerk laundry
William S Hedley Jr 17 12/1882 NJ Wales Wales plummer
Robert G Hedley 14 12/1885 NJ Wales Wales at school
Richard B Hedley 13 3/1887 NJ Wales Wales at school
William REYNOLDS 21 10/1878 son-in-law m1yr NJ NY NJ clerk railroad
Harriett I REYNOLDS 23 10/1876 dau NJ Wales Wales m1yr 1 child, 1 child living
Josephine A REYNOLDS 2mos 3/1900 grdau NJ NJ NJ


Diana in AL