I'd advise against taking the kids - when I had to have my cat put to sleep, he had a few involuntary motions that freaked me out, and I was in my 30s. It still kind of haunts me, to be honest.
I'm so sorry you have to make the decision - it's the hardest one I've ever had to make and I've been through it four times (two were my animals, two belonged to my mom).
When I had to have my dog Bear put to sleep, I sat on the floor with him (he was a big shepherd collie mix), his head in my lap and just petted him. That way, he knew I was there and he was loved. (I'm tearing now just writing this, and he died in Nov. 2002.)
I wish I thought of a paw print, but I have his ashes in a nice little box, along with his collar and favorite toy on a shelf in my office. That way he's always there, just like in life.
The day we had to do it, I was a mess. I went to take a nap and my husband, trying to be helpful, cleaned out all of Bear's stuff. I was kind of upset at the time, but I understood
why he did it. He didn't want me to have to do it, but honestly - I'd rather have been the one because Bear was my dog before we got married.
I'd say prepare yourself to hear and see them for a while. The first couple of nights were the worst - I kept hearing him and I'd swear I could see him. My mind played tricks on me to the point where I would have sworn I saw his tail vanish around a corner and it was so
real, like he'd just gone into the next room and I'd see him if I was fast enough. It was odd.
It's a sucky thing to go through many
to you.