I have an idea: split the garden and mansion areas from the surrounding nature reserve; tag the former as a park, the latter as a nature reserve (named Allerton Natural Area); and unite them as/within a relation.

Also, the official website calls the place "Allerton Park & Retreat Center", not "Robert Allerton Park".

I'd do this all myself, but I'm relatively new to editing OSM, so I don't want to mess something up.