An outside cat and kittens would not be safe in an open box. They will go hide somewhere that they think is inaccessable to others. When we had unspayed barn cats, they would have the kittens in the hay. That way, they felt they were safe from predators. If your cats were to have kittens in open boxes, any tomcat could come along and kill them (sad, but true, that tomcats sometimes do this).
The reason I ended up getting all my outside cats fixed was the number of kittens who didn't survive. One went too close to the dog, who killed it. Several were born in the winter, and as soon as they were old enough to get out of the nest, they wandered off and froze. Then I lost one Momma in childbirth...of course the kittens she had already given birth to passed away, too.
These are the realities of outside cats having kittens. And this is in a "safe" place where they had access to a warm barn. If that is the only care you are able to provide your cats, that is the risks involved to them. I do still have outside cats, but I will never have another outside who is not spayed or neutered. Life is just too cruel.
I'm sorry your cats are destructive inside. But to me, if you can't provide them a safe place to give birth, you should consider giving them up to a rescue. Read through some of the posts here...sometimes there are problems with the birth. That will be extremely difficult for your kids!
At the very minimum, you need to be sure to take these girls in to be spayed when the kittens are six weeks old. I know you must love your cats, so at this point you need to think about doing what is right for them.
It took me some time to understand why continued breeding of the cats is such a bad idea. I also cared for my Mommas, and found homes for their kittens. But there are so many many cats in this world that are unloved and unwanted. The only way to slow that down if for responsible people to spay and neuter. Count up the number of kittens you have allowed to be born by not spaying your pets. It becomes a little scary in a short time, doesn't it?
Whether you can bring the kitties in, and place them in a dog cage, or not, I hope you will stay here at TCS. Maybe you will learn quickly, what it took me a few years and losing too many kitties to learn!