Jean,
this may be your family in census 1890, though Reinhold is listed born 1868.
Home parish: Upsala
Residence: Od
County: Uppsala
House-owner Anders Persson Tunell b. 1836 in Hökhuvud parish, Uppsala county
Wife Gustava Andersdotter b. 1841 in Skäfthammar parish, Uppsala county
Son Leonard b. 1864 in Hökhuvud, commercial assistant
Son Carl Johan b. 1866 in Hökhuvud, tradesman
Son Reinhold b. 1868 in Hökhuvud, tradesman Daughter Emilie Josefina b. 1870 in Hökhuvud
Son Joel b. 1875 in Tuna parish, Uppsala county
Daughter Elsa Maria b. 1870 in Tuna
Son David Efraim b. 1885 in Tuna
Census 1900:
Home parish: Alster
Residence: Snårstadstorp
County: Värmland
Tenant, former house-owner Anders Persson Thunell b. 1836 in Hökhuvud
Wife Gustafva Andersdotter b. 1841 in Skäfthammar
Daughter Emilie Josefina b. 1870 in Hökhuvud, dairy woman
Daughter Ester(!) Maria b. 1880(!) in Tuna
Son David Efraim b. 1885 in Tuna
I would suggest that you contact Landsarkivet (Regional Archives) in Uppsala (
www.ra.se/ula/english.html) for further information - they can tell you if and when this Reinhold emigrated.