Not my exact advice, but here's another option.
Approach dd18 calmly and give her permission to allow her father to buy the dress.
The vibe I'm getting from this is that gf and dd18 constructed this plan somewhat together. she wants the dress. gf wants to look cool. dd18 isnt mature enough to realize that you will see through their strategy. One way or another, Im sure they both really want her to get that dress.
Either don't respond to the email at all, or respond and say "I will discuss this with dd, thank you. I probably wouldnt even mention to whole coffee invitation.
Short and sweet baby.Surviving is important, thriving is elegant- Maya Angelou
you is kind, you is smart, you is important