While I agree that "you get your own man" if you have a separate man from the one the other party is using, I, as a lawyer, disagree with the comparison being made to using the same lawyer in a divorce. There, the rules are very clear, from a lawyer's perspective, and poorly understood by non-lawyers. The obligation to protect their interest arises with each client, so there can be none of the type of preference JD suggests. To do so would leave the lawyer exposed to complaints to the Law Society, and/or negligence suits. Even in the US, where respect for the legal profession is low, the duties faced by the lawyer exist, and are scrupulously followed (except perhaps on TV). The moment a conflict arises between two of the lawyer's clients, he must cease to represent either party without the express consent of the other.
So in your example of a divorce, (simpliciter, with no issues that require a Judge to resolve them) where only one lawyer is involved, there are always signed consents by the parties, allowing the lawyer to represent both sides. In such cases, where the parties have divided the spoils according to what they thought was fair at the time, only where there is a misunderstanding of the role played by the lawyer will you get the parties later thinking the lawyer represented the other side to their detriment. The fact is that such complaints and general perception about lawyers are frequent, demonstrating my point that the rules are not well understood by the public at large.