Our whole family has taken tkd at times- the kids did it for a while, then DH did it, then I started up and took the kids back- at the moment, none of us are going, and I do miss it. But wierd work schedules have gotten in the way.
A few tips, to go along with what the others have said:
For a kid, I'd think you want an ATA school. They have a pretty standard "curriculum". Your oldest would probably go into the regular beginner class, and the youngest into Tiny Tigers. So you will be camped out there for a couple of hours. Bring a book.
Tkd is not the cheapest sport you can pursue, just warning you now. It's not just the lessons. They will do testing about every 8 weeks and that's about $50 per kid. They will encourage you to go to tournaments which can get pretty pricy. Once the oldest hits camo belt, you'll need sparring gear (ebay is a good option) which new will cost about $200. At some point you'll have to buy practice weapons. It seemed like every time we turned around, there was more money needed. Some schools have a Leadership program which costs extra, or they do special workshops or summer camps. It can add up very quickly.
Some schools offer a "deal" if multiple family members sign up. Ask about it. At our school, I took for free because both the kids were signed up. I am so not a taekwondo person! You know in every class like that, not just taekwondo but dance or swimming or sports, there is that one
complete dork that you just feel bad for?

That would be me. But it was good exercise and everyone was friendly and encouraging.