You should take a more thematic approach and stick with openings that follow general principles to the letter. The two best for that are the Ruy Lopez and Queen's Gambit Declined. Don't go into theory.
For example, the Ruy Lopez:
1.e4 - Take control of central squares (d5 and f5) - Important to note that White does not control e4. Control and Occupancy are NOT the same thing
1...e5 - Take his share of control of the center (d4 and f4)
2.Nf3 - Attack Black's loose pawn
2...Nc6 - Defend Black's loose pawn
3.Bb5 - Attack the Defender of the loose pawn
3...a6 - Recognize a tactic, if 4.Bxc6 dxc6 5.Nxe5, Black wins the pawn back with 5...Qd4, therefore, nudge the attacking Bishop
4.Ba4 - Recognize that Bxc6 doesn't win a pawn, and hold on to the Bishop.
4...Nf6 - Attack loose e-pawn
5.O-O - Recognize that Black's King is still on the e-file, and opening it with Nxe4 may be very dangerous for Black
5...Be7 - Notice that Black still has the Qd4 trick if White tries to win the pawn.
6.Re1 - Protect the loose e-pawn.
6...b5 - Recognize that Bxc6 and Nxe5 is now a threat because e4 is no longer loose.
7.Bb3 - Uh, obvious? I'd hope so!
7...d6 - Add cover to the e5-pawn, what is known as Black's "Strongpoint"
8.c3 - Prepare d4, the other central pawn.
8...O-O - Bring the King to safety
9.h3 - Think a move ahead and realize that 9.d4 Bg4!, pinning the Knight to the Queen and virtually removing a defender of d4, makes the d4-pawn somewhat weak.
Notice how none of this is memorization, and for all 17 half-moves, if a child asks why to a move, the answer is there, unlike many more complicated lines like the Najdorf or King's Gambit where the only real reason why is that it's what everybody plays, and that there is no rational explanation. Not the case here with the Ruy Lopez, and the same goes for the Queen's Gambit Declined, Orthodox Defense.
I have offered to help the kids at my girls grade school.
Any thoughts on openings? For instance, it's a lot of fun to win, but winning on an opening trap doesn't exactly teach you much other than rote memorization.
So, I love the Kings Gambit, do you think it's OK for 7-9 year olds to pick up? Or should I be sticking with more "set-up" and "thematic" openings like the KIA?
Defense, it seems important to learn to defend in the open games, but the sicillian teaches a lot about dynamics and tactics.
I guess I would like to see them learn good fundamentals and am trying to figure out what openings teach those the best.