One collection of Taylor Orphan Asylum records, 1867-1943 (Call# Racine Series 40; acquisitioned in 1973), is now owned by the Wisconsin Historical Society, but is held at their Area Research Center at the UW-Parkside Library in Kenosha. See www.uwp.edu/departments/library/archives/
for contact info. Apparently this collection does not include records on all resident children, but only "for some years, lists of directors and resident children." But it might be worth checking this collection if other records aren't at the Racine County Historical Society.