Is there any authority on a county level to keep a member of the commissioners court from voting on any matter that may be related to an act in which the member is involved in a pending criminal investigation and prosecution?

How's the commissioner involved in the investigation? The only thing I can think of is the statute requiring abstention in cases of conflict of interest.

Under section 171.004 of the Local Government Code, if a commissioner has a substantial interest in a business entity or real property, that official must file an affidavit with the county clerk stating the nature and extent of the interest. The commissioner must also abstain from participating in the matter if action on the matter "will have a special economic effect on the business entity [or real property] that is distinguishable from the effect on the public." A violation of this affidavit and abstention requirement is a Class A misdemeanor under section 171.003.

So if the commissioner owns a business or property that relates to the investigation, and the commissioners court will take action that would affect that business or property in a way that's different from how it would affect the public, that commissioner must abstain from discussion or action on that action. If he doesn't file the affidavit and abstain, he could be prosecuted.

Note that per section 171.006, such a violation does not make an action of the commissioners court voidable unless it would have passed only with the vote of the person who violated the requirement.