Some issues that you need to consider. You are going from a multi-member LLC to a single member LLC. This will have some "holding period" issues. IRS Revenue Ruling 99-6 address the tax issues regarding the conversion to a single member LLC. It is often better to have a nominal LLC member (i.e 1% owner- wife or kid) before the LLC membership purchase or the LLC membership redemption. Whether you decide to have a redemption like you contemplate also has tax issues. Is it better to have redemption (where the LLC buys) or a purchase (where you buy) depends on the underlying assets of the LLC and how long you have held them. To answer that, any tax professional would have to look at the LLC tax return and the depreciation and amortization schedules.
This is really a question of the difference in the tax treatments for each buyer. If you buy her interest than you are increasing your basis in your membership interest in the LLC, (but not your capital account). If the LLC buys back her interest it does not affect your basis in the LLC. As far as the tax treatment to your partner I suggest you bring copies of the LLC tax returns and the LLC operating agreement to a tax lawyer so that they can advise you on the proper and most efficient tax treatment.
The above statements are provided as general information and not intended as legal advice. Each matter has its own set of unique circumstances that cannot be adequately addressed without consultation. You are strongly advised to hire an attorney licensed to practice law in your state to represent you.
Your question assures me that you need another tax adviser. Go get one and find the answer. It will depend upon a number of factors, such as tax basis, undistributed income, and maybe more. In any case, don't go fishing for advice about something this specific.
The advice provided is in good faith but not a guaranty of accuracy under all circumstances.