I think the idea of giving him a safe place to chill out a bit is an excellent one.
It might also be a good time to sit down with both children and try to teach them how to understand, and react to (and when not to) animals.
(and this is not directed to you, it's my basic opinions in general).
There are so many innocent animals put to sleep every year because children are not taught how to have a healthy respect around them, scare them, and end up scared themselves, bitten or worse.
We teach kids not to talk to strangers, to yell "no" when needed, not to touch the stove, and all other sorts of things to keep them safe, but it is rare to find a healthy respect for animals in that group. Because bottom line, even the most sweetest, gentlest, loving, affectionate cat (or other pet) may attack if feeling in danger or cornered. They simply do not have the cognitive ability to assess a situation and to make a value judgement on who is scaring them. They just react instinctively to danger. I've always called it "the attack frenzy," (even though I've only seen it 2 or 3 times).
Perhaps it's also time to sit your two kids down (you didn't say if the 6 year old was a boy or girl), explain to them the things that frighten animals and to avoid doing those things around them (yelling, fast aggressive movements, cornering, forcing them to be picked up, watching for body language -- ie, they see a cat's tail switching back and forth, that means "go away!".
Iwould also teach them never to approach a strange animal, whether with a person or not. And if the do have permission, to simply put out their hand PALM UP, call the animal, and first see if the animal comes to them. So many time children get so excited and will approach an animal too quickly, which can spook the animal.
Your daughter was doing what she thought was right by picking up the cat to comfort it based on human standards, and she was doing what she thought was a good, kind thing. So if we teach our kids that animals think differently than we do, that what comforts us may scare them, and how we can best comfort the animal (ie, walking away is better for them than trying to hold them because they don't understand it the same was we do), it can avoid these kinds of problems in the future.
It's also a way to take her guilt away because she was doing what she thought was a good thing, and that's what counts. She was showing love and compassion, and the only difference is she was showing it in a human context. Once she knows how to do it in a cat context, the problems will most likely be solved.
I believe a 6-year-old, even younger can understand those things. And I think children are also very able to understand they those things scare the animal, that you are teaching them things that make the animal happy and trusting, and most children would want to do that.
With younger kids, you could even do role-playing, with the kids taking turns being the "kid" and the "cat" (or dog or whatever).
Then I'd then teach them how to react if an animal seems afraid. (and understand, I am not in any way saying this was your fault, just as an explanation). If your daughters know in the future that a scared can be dangerous , and the thing to do is back off and walk away for a few minutes,
Come to think of it, I sorta like that idea. LOL I might write out a possible proposal and submit it to the shelters, rescues etc, to go into schools for presentations. Might be interesting and fun. They do it for fire safety and lots of other things, and I think the number of children hurt by animals each year would make it valid.
The same way we give our children rules for what to do if approached by strangers, or any other dangerous situation, I think we should do the same when it comes to animals, whether they live with us or not.
I do think this is probably a one-time situation, and your cat will get over it and all will go to normal. I had a cat at one time that attacked me every time I brought another home from the vet. I would throw her into the closet for a few hours. When I finally opened the door, she would walk out purring and rubbing against my leg like nothing happened. Eventually she grew out of it, and was probably the most clingy, affection cat I've ever had until she died about 4 years ago at the age of 22.