Not sure if you ever got any ideas on a theme for your adoption party and I couldn't find the post for some reason. Kind of random but what about fish? You could have signs/banners that say something like "It's O-fish-al" or something like that? You could use swedish fish as a favor or decorations/snacks on the tables.
My only other thought would be something about "A Perfect Combination" by combining you, DH and DD. But I have not been able to come up with any type of decorations with that theme. Maybe something with all 3 of your initials?