Hi there! I'm currently working through older tickets, and upon re-testing this issue, I've come to the conclusion that Max Quake (Earthquake) does not allow you to target an opponent regardless of whether or not your first pkmn used regular Earthquke.
1) (using pkmn from another test) Gave myself an Arbok and a Tentacruel, both lvl 40 with Earthquake, Mud Shot, and Sand Tomb. Tentacruel was given 10 dynamax candies.
2) The opponent NPC was made with the doubles rule enabled, with two unrelated pkmn.
3) Selected Max Quake (earthquake) on Tentacruel (was not able to choose a target), and regular earthquake on Arbok.
4) Tentacruel used Max Quake on the opponents first pkmn, and both of my pkmn's spdef increased. Arbok then used Earthquake and damaged both enemies and Tentacruel.
It seems that any regular move that would normally hit "all adjacent pkmn" to the user, when turned into a Max Move, will not allow you to choose a target. I tested Earthquake (Max Quake), Bulldoze (Max Quake), and Brutal Swing (Max Darkness), and none of these would allow me to select a target. I, therefore, assume all of the moves from the "Double Battle - All other pokemon" list (https://bulbapedia.bulbagarden.net/wiki/Double_Battle
" would have this issue. The moves listed in the "all foes" list did not seem to have this issue, as I was able to choose my target with moves such as "Max Ooze" (Acid).
As such, I will go ahead and move this issue to internal! Thank you!