Assure your children that Monroe LOVES them! He just doesn't know the best ways of showing it yet. Think of him as a toddler who doesn't know yet how to get along with the others in his play group.
I believe he is feeling more comfortable, after a month and a half at your house, and he would like to play with you! If you were a cat, you would nip him back. Cats play that way all the time; it looks and sounds as if they're killing each other, but they're having fun. Monroe is probably a little surprised that you all don't go for it.
My fifteen-year-old cat still does it. She'll be happy and purring as I pet her, and then she'll go after my arm. I have to call it a love bite. She has the best intentions. But I don't like it.
A "Don't!" doesn't work as well for a cat as it does for a dog, but say it anyway - loudly. It will at least annoy him enough to be distracting. A squirt of water might help Monroe decide he doesn't want to play this way with you, if you can squirt him fast enough. Your response of moving him into another room seems to be working, too; you've distanced him from those he loves, and he's taking the correction for a while.
The easiest solution might be good cat toys.
Cats think good toys are anything that interest them (including your body parts - but you already know that), but you need to ensure that his toys are safe. Balls, toys from the pet supply store, cardboard toilet paper rolls, even an old-fashioned *paper* grocery bag without handles (he could get his head caught in handles, and plastic bags are dangerous) might be fun for him. My cats have loved all those at various times, plus socks, pens on desks, and anything in a half-open dresser drawer. So I have had to be careful how I open drawers.
If you can have little baskets with a few toys in them placed about the house, then your daughter or any other family member can grab one and distract him that way. Having toys also makes it possible for your children actually to play with Monroe without fearing for their personal safety.
As Monroe gets older, he probably won't "attack" as much (my cat is rather an exception); it's just a matter of living through this stage and planning how to respond.
You can also call your vet; you might get some more suggestions. This may well sound like a complete nuisance to you, but it's just part of caring for a cat, and you'll be happy that you took the trouble. Monroe sounds like a winner.