Ed,
I suggest that you first learn the exercises (warmup) and aiki-taisos of Aikido (ikkyo undo, funi koga undo, etc. ..the Aikido teacher can explain that) and then give it a go.
Just like there's no "home surgery kit", there's no "home Aikido kit" either. It takes some instruction and some practice other than casual observation.
I came from striking arts to Aikido, but luckily, I had ukemi training (force dissipation by falling) with Judo, so the transition was easier for me, but it's a different skill all together than hitting arts. Where karate is a "force delivery" art, Aikido is a "blending with the force" art, so your intent is different.
As Eyrie said, it's a different mental concept, and it's powerful. Strangely enough, as you train in karate, you reach the same type of methods and ideas as you get to "the top of your game", and actually do a lot of "Aikido-ish" things as you get into higher levels of karate.
I did a seminar about a month ago where I used karate as the attacking method of the uke when I was teaching. The simple act of redirecting the energy negated most of the dynamic of karate and completely destroyed it's "foundations" (stances). My "students" were 9th and 10th Dans, 2 6th Dans, and a couple of underbelts... and they all met with the same success against this different method... in a word, none.
What's interesting, is that the basic concept of Aikido is based on the same thing that karate is... the arm sword. Like different styles of karate, it's used differently in Aikido, and for different purposes. As Eyrie said, it's redirection and cutting (as in swordfighting), and the only thing that's actually different from karate is the footwork and redirection of force, rather than the delivery of force(if your karate is correct). Of course, there are "nuances" in it that are different, but you have to lose the skepticism for a few minutes and understand how to generate that "internal pressure" you argue against all the time (ki).
I would suggest going to class with your kids for a few weeks, and get a little instruction. You can probably trade off some Aikido training for karate training with the Aikido instructor. I think you'll enjoy it, and it might not be as frustrating once you have "peeped under the sheet".