Does a private backyard party on our own property need an ADA porta potty?

Private invitation-only parties at a private home usually do not fall under the ADA portable toilet rules that apply to public events.

Title III of the ADA covers places of public accommodation. A backyard graduation that is invitation only, has no tickets, and is not open to the public is typically treated as a private social gathering at a residence, not a place of public accommodation. The 2010 ADA Standards rule about providing at least one ADA unit when portable toilets are clustered is aimed at sites that already have to comply, not at every private house party.

Your quote sheet pushing an ADA unit next to the standard unit is still sensible in your case because you already know a guest uses a wheelchair and the house bathroom has steps. That is guest access, not a public-event mandate. Put the ADA unit on firm, level ground with a clear path from the patio so the relative can actually reach it.

Local temporary-use or gathering permits can still add their own restroom conditions, so check that separately if your city requires one. For the ADA question itself, private property plus invitation-only usually means the public-event ADA toilet percentage does not apply. Providing the accessible unit for your guest is the part that matters.