I understand your concerns both about your current dog as well as your children. Also, you have gotten a lot of good advice.
We adopted Omar (in tact) and brought him into our house where we already had Magnum (neutered). Magnum was three and Omar was about to turn two.
A lot of it depends on the temperment of your first dog. Magnum is extremely passive and laid-back. He loves other dogs sooo much that I knew he'd be fine with another dog - even male.
He submitted instantly to Omar, as I knew he would, but we still had to let Omar state his position as top dog. It was hard for me to watch Omar dominate Magnum, growl, etc..., but I had to let it happen. I was right there though, in case I needed to step in.
I was very nervous about Omar marking my house. He didn't though, and I praise God. He does pee on everything outside though, but so what. Although, I don't have a real Christmas tree and I don't have any plants that stand on the floor. That may be my saving grace.
As for the weinie thing... I know - it's gross. But, boys will be boys. What can I say. Magnum is fixed, and it still comes out. Omar's does too and he we haven't fixed him. We just tell them to put their "pink thing" back and laugh.:rolleyes:
As for your children, since you already have a dog, they already know how to respect and treat dogs which is a major advantage. As long as they respect the rescue like they do your first dog, you should be fine. The fact that his brother does good with the child in his new family is a good sign. Just keep an eye on everything.
My advice...
1. Make sure the rescue dog has plenty of time to get adjusted to your house and family. It's going to be the equivalent of a child walking into a new classroom. He will be scared. All he understands right now is that for some reason, the people he thought were his family have let him go. Let him have some time alone too like the other person said to get accustomed to the noises and smells.
2. Keep their food separate at first until you see how they do together. You might want to get some new toys for the rescue dog so your first dog doesn't feel threatened.
3. The trial period is a good thing to have to fall back on. We had one too. You just don't know.
4. That was very good advice about the left-over sperm.
Good luck. Please keep us posted on how things go. I am never sorry that we adopted Omar. They are best friends and so much fun to watch together.