But I've done hundreds of dog introductions myself (another place, I don't work here), and owners can have unrealistic expectations and views of what they see when their dogs meet other dogs.
Workers who do these introductions look at the interaction objectively; and it's good to see they are able and willing to say no if they feel there would be a problem.
It sounds (according to your own statement) that they had a roomful of dogs, so they must be doing something right - and are keeping those dogs safe from potential problems.
You say you work a lot, and that you have a young dog; so I have little doubt that your dog is just filled with energy to burn; and it is good of you to look for a place to take him.
You were clearly given another alternative by Second Home, to board him - which might have given your dog a chance to come and go from Second Home a couple times, getting used to the place and maybe facilitating another attempt to get into daycare later.
Be a little more reasonable with your expectations of a place like this; and maybe don't jump to personal attacks suggesting that they don't want to work hard, just because you bruised your own ego.