You have not provided sufficient facts to provide a definitive answer. For example, it could be that the 2nd attorney could not achieve a better result for you simply because the 1st attorney had so badly "botched" the case. If so, you may still have a legal malpractice claim against the 1st attorney. Furthermore, "personal relationships" among the plaintiff and defense attorneys can cut both ways. Situations can and do arise in which the plaintiff's attorney can obtain a better resolution for the client, more quickly, if he/she has litigated against the defendant's attorney in the past and the two of them have a "relationship" of mutual professional respect. Thus, depending on the nature of the "personal relationship," the attorney may or may not have a conflict of interest. If there is a substantial possibility of a conflict of interest, then the attorney has a duty to make full disclosure to the client of the underlying facts that create the conflict, as well as the legal ramifications of those facts. RPC 1.7. The attorney must also advise the client to seek the advice of independent counsel concerning whether to waive the conflict of interest (if it is what is termed a "waivable" conflict, which would also depend upon the facts). If the attorney does (or did) have a conflict of interest and failed to take those steps, then you could have a potential claim against the 2nd attorney. Many States allow you to settle the underlying matter and still pursue your potential legal malpractice and/or conflict of interest claims; however, I do not know whether California follows that rule. Attorneys also have an obligation to account for all funds they receive and distribute on the client's behalf. The client is absolutely entitled to see the underlying bills charged the client's account. That would include copies of the bills/invoices from the "experts."
Also, California, as I recall, has a relatively severe one year statute of limitations on most such claims. So you should consult independent counsel promptly if you believe you may have potential claims against either or both of these attorneys.