Not pretending to explain all possibilities of combat patches. Just the one possibility being explored here to explain the 2nd Army patch. A separate brigade is sufficiently large enough to qualify as a command unit for the wearing of a combat patch. With the rules established in 1945, it is the smallest unit. The rules changed in 2014 to allow units as small as a company.
When serving under multiple commands, it is the soldiers choice which patch they wear.
My particular company was under the command of the 79th ARCOM which was a reserve command in the states. We had no individual company patch. During Desert Storm we were as a company, assigned first to the 3rd Army and later to the 22nd SUPCOM so we have the option of wearing either.