As an owner of 3 dogs, all small, I have a few opinions! :grin:
I had a situation arise very similar to yours! I had two dogs, and a friend (with a dog whom I loved!) said they needed to give her up; she was terrorizing the cats.
I thought about it long and hard. I decided to adopt her.
It seemed to be a mistake at first; one of my dogs didn't seem to like her. She spent a LOT of time just wandering around the house whining!
The whining, pacing, etc. went on this way for at least 2 weeks, I wondered if I'd have to give her up myself (although never seriously considered it, I was so attached to her at that point).
That was in February. She is still a bit of a whiner, but she is now comfortable here, and my dogs have adjusted. It took months for her to truly make our home HER home.
What I am trying to say, is that a trial period isn't always indicative of how the dog will do in your home. It is a smart idea, don't get me wrong. But ESPECIALLY when a dog is used to one home, then goes somewhere else, there are extra adjustments to be done. I think just due to all the changes, and fear of abandonment, and getting used to new people, and missing your "old" people. But dogs are very adaptable.
I think the best thing would be for your friend to visit your home with the dog, and let the dog get to know you, but NOT stay.
Then an overnight visit, to allow more time together, and finally a nice big trial period.
I am probably more cautious than most people, but I have seen dogs who've developed behavior problems due to abrupt changes in their lives. So I am all about giving them the best chance at a happy life.
I don't know if my suggestions are feasible for you, but good luck with whatever you decide to do!
And remember you to expect setbacks, they are normal with big changes like this.