Apparently when Herman remarried after the death of his first wife, he had his oldest 3 children go to the United States. They were on the same ship as our Ernst Conrad Wehrmeyer, the barque Union which arrived in Baltimore in October 1860. The oldest child, Elise (Christine Elisabeth) was 18, Henrich, age 15 and Herman age 9. There were other relatives already in the United States that they could go to live with. Other Brinkmieiers (relatives of his first wife) were already settled in Ohio or Indiana.
Herman emigrated to the US Oct 1865 with his 2nd wife and 5 children

1880 Indiana, Vanderburgh County, Evansville, ward 6, E.D. 89, p. 13A, stamped page 488 (taken 5 June 1880)
204 Read, dwelling 108, family 116
Nemeier, H.H., white, male, age 28, head, married, moulder (stove), born Germany, parents born Germany
———-, Sofa, white, female, age 28, wife, married, keeping, born Prussia, parents born Germany
———-, Elizabeth, white, female, age 6, daughter, [single], born Indiana, parents born Germany
———-, Emmy, white, female, age 4, daughter, [single], born Vanderburgh Co., Ind.
———-, Lidia, white, female, age 2, daughter, [single], born Vanderburgh Co., Ind.
———-, Ernst, white, male, age 21, brother, single, moulder, born Prussia, parents born Germany