I can't tell you how to crate and rotate. I don't know you, I don't know your dogs, I don't know the dog you are trying to integrate into your family, and I don't know the layout of your house. I can tell you how I crate and rotate, though.
For the last week, my home has been in the midst of what I call "full lock down" crate and rotate. This means that dogs don't even get to see each other. Now, I'm not fooling anyone here: my dogs are well aware that there is a stranger in their house, and Abe knows that the other dogs live here as well. The point of "full lock down" is to give the dogs a chance to gather information about each other without forcing them to interact. It's breaking introductions down into the smallest possible steps. The smaller we can break down introductions, the less overwhelming they will be. The less overwhelming introductions are, the higher the chance of success.
I have nothing to lose by going slowly. I have everything to lose by moving too quickly.
The crate and rotate set up in my house involves several baby gates. In lock down, the baby gates are covered by blankets. For us, the first step in relaxing our system is to get rid of the blankets. I start by pulling part of the blanket away for fifteen to thirty seconds. I'll do this three or four times the first day to make sure I'm reading all the dogs' signals correctly.
What I like to see is that the dogs notice each other, maybe sniff a little, and then move on with their business. That's perfect. The dogs are telling me that everything is cool, and they're ready for the next step.
Sometimes, though, that's not what I get. When I brought Marnie into our house, she completely ignored the dogs on the other side of the baby gate. No sniffing, no looking, no interaction at all. Marnie, if you remember, had anxiety around other dogs. When I started pulling away the blankets, Marnie started playing ostrich - if she didn't notice the other dogs, they weren't really there. If they weren't there, she didn't need to be afraid of them. Marnie was sticking her head in the sand. She wasn't ready to push things further, so she stayed at the "brief glimpses" stage of the Staycation for several days (almost a week, if I remember correctly). When she started watching the other dogs, I knew she was ready for the next step.
Another common reaction to seeing each other at the baby gate is that dogs will start to play with each other. I'm not crazy about this behavior, but I'll take it. Play indicates a higher level of arousal; the dogs are more excited. For our socially awkward bullies in particular, there's a fine line between play arousal and fight arousal. I want introductions to be as boring as possible. If dogs start playing, often I'll hang out here for another day or two to see if they calm down.
The last behavior I commonly see at this stage is that dogs will get tense and start to snark or fight. The moment I start to see tension between the dogs, I cover the baby gate again. This pretty clear language from the dogs: they're not ready for this stage. If I get tension or snarking, I cover the baby gates and don't uncover them again for at least another full forty-eight hours. Remember, I have nothing to lose by going slowly. The dogs will tell me when they're ready to move on.
So how did Abe do? Well, he sniffed at the baby gate, watched the other dogs for a moment, and then wandered away to go chew on the buckle on my backpack. My dogs didn't even bother to get up from the couches. Perfect. Well, except for my poor backpack.