Can a conservator and guardian stop family from visiting in a nursing home?

Yes, if reason is valid. For example if a son with a drug problem is coming to get mom and take her out to the bank to get money to give to him or a granddaughter with a history of stealing keeps coming and grandmothers jewelry keeps going "missing" after the visits, or if a husband with a history of abuse wants to visit and has anger issues....all kinds of reasons that it might not be a good idea.

If the guardian has valid, demonstrable reasons for believing that the visits are detrimental to the person's wellbeing, yes.

Would you like to say a little more about the situation you're dealing with?