If I understood your query properly, The First Team (lets call them Team 1) is the one that chats first, correct me if I’m wrong.
So on your website, on the pages that should be connected with your Sales Reps from the Team 1, you’ll need to install the Group for Team 1. At that point they’ll be the ones to answer the queries of your Customers first. Then if they’re job is done, and there’ll be the time for the Team 2 to come to do their job, proper Agent from Team 1 will transfer the chat to his/hers Partner in the Team 2, that has his/hers own Group (If you name the Groups after the only Agent that is in it, it will be much easier to manage).
The Group doesn’t have to be assigned with a URL rule for it to work as a transfer inbox.
As you already noticed, there can be only one Group assigned to one URL.
I hope, that this workaround would work for you. Right now as we’re preparing something new for our Customers, we will disscus your case further with our Dev Team.
Thanks a lot for your feedback and insight into LiveChat