I find it can be very overwhelming for the dog and a lot of pressure to expect for them to not bark at each other etc (not my expectation but that of many people i have met)
If a guest dog is going to be at my home, then he/she has to meet my dog as well. That's a key part of the vetting process, i.e., seeing if the dogs get along. Some people have their dogs meet outside on neutral ground. However, my dog is leash aggressive so it is far better to have the dog come inside. Also, my dog typically is more interested in the human than the accompanying dog. I like to see how they interact, if at all. I've had dogs come over who only check out the house, sniff around everywhere and pretty much ignore my dog and he does the same.
From your profile, I see you not only have small children, but also a Boxer and a cat. I would think it critical to find out if any guest dog(s)--since you will accept 3 more--can handle the situation and vice versa, unless you have a separate boarding facility and none of the animals come in contact with each other.
With 2 Boxers, a cat, and a 4 year old, and 6 year old child, I completely agree that it needs to be assessed during the meet and greet IF it's a good fit.
I prefer to have the dog come to my house and meet my dogs. We host often, and my dogs are comfortable with a new dog just walking in the door. I always ask the client what their preference is, as they know their dogs best. Some do OK to come right in, others do well to meet outside. Others do best to meet in the cul-de-sac on my street and walk to my house. I'm flexible, provided I feel safe, and the dogs are safe. I see Meet & Greets as a way to measure the guest dog, the client, and the interaction between the guest dog and my dogs. Listen to your gut. If something happens that turns me off from watching a dog (or if the owner is just that unreasonable, etc.), I'll say something along the lines of, unfortunately, based on my experience, I don't think I'm a good fit for you. (I always make it about me.) They will often ask why, sometimes desperately. I'll rephrase, and say something like, though I've only been with Rover X time, I've been watching dogs for X time, and my experience tells me I'm not your best option. I always leave them with other options, such as another Rover sitter I'm familiar with, or a boarding facility nearby or two.
I currently have two small dogs and a bird. I always do the following for meet and greets.
1st one: on neutral ground - usually at the park near my house.
2nd one: in my house. This way my dogs are already familiar with the guest dog before it comes into my home. They don't feel like they have to defend the house. Also - this helps the guest dog feel comfortable in a strangers home since their parent will be there. Cold drop offs for boarding never work or they take a long time for the guest dog to warm up.
In addition, if it's an extended boarding booking (7+ days) I usually recommend the following after the meet and greets:
1 daycare and 1 night of boarding leading up to the long stay. It's a nice progression to get the dog comfortable with you. You usually find out any red flags/quirks/concerns on the 1st day of daycare and can work on it with the pet parent since they are still in town.
Usually pet parents love this idea and they are willing to spend the money to take their dog super comfortable with you before they take off.
Best of luck!