Guardianship and conservatorship are governed by state law and as a result the issues and answers raised by this question may from state to state. However, certain principles will likely apply no matter what state is involved. First, when a petitioner applies for establishment of a guardianship, if all interested parties consent, the likelihood of an order of incompetance and an order appointing a guardian being entered more rapidly could be increased significantly. Interested parties usually include at least a spouse and any adult children. Sometimes additional relatives (parents, siblings, etc.) may also be considered interested parties. However, despite the consent of all interested parties, if the proposed ward cannot or will not consent, then in most instances a court will still require a professional determination of incompetancy before removing the ward's rights.
The mother in this situation may wish to have her own representation since the guardianship could impact her if she loses control of her spouse or of martial assets which get pulled into the guardianship.
As to any living trust and how it will be distributed, that will depend on the terms of the trust itself as well as the circumstances of the case. Since the guardianship court is usually a court of equity, the court can apply principles of fairness in providing for both the ward and the ward's spouse. Ultimately, because guardianship proceedings involve complicated issues, having experienced legal representation is important.
You probably have your answer about the GC (guardianship/conservatorship) process by now, since your question was posted three months ago. At this time, assuming a GC has already been appointed, the focus probably needs to be directed to your parents' estate plan. Your father was probably a co-trustee with your mother. He needs to be removed, in accordance with the terms of the trust. I would strongly encourage you to have an estate planning/probate attorney review your parents' estate plan and make sure (1) the trust is being properly managed, (2) trustees are appointed, (3) financial institutions are notified that your father is no longer trustee (so he can't continue to spend money). Now is also a good time to start thinking about what could possibly go wrong after either or both of your parents die. For example, is it possible for an overly friendly neighbor to convince your mother to change her estate plan and disinherit the children? How will personal property be divided? (For instance, can copies of family photographs be made now so as to prevent fights later on?) Will all children/beneficiaries be treated fairly? You can read general information about trust administration at http://www.delougherylaw.com/CM/Custom/FAQ-Probate-Estate-Administration.asp.