Do children have family decision-making rights over a spouse?
My father is married to his fourth wife, and he has four children from his second wife. Do we have rights to any decision making?
That depends on whether your father is competent, has finalized any legal documents directing decisions—and most importantly, on what you want to decide.
As long as your father is considered legally competent—basically, able to recognize and understand his legal rights and any documents that might control them—he alone has the right to make decisions that relate to his care and finances.
If he becomes incapacitated, things could get a bit messier, as you seem to know. If he is unable to express his own wishes for his medical care, for example, doctors and other medical personnel generally defer to the present spouse for direction—although the more sensitive ones will also listen close relatives such as children.
And if he dies without leaving a will, the property he owns at death will be divided and distributed according to the formula set out in state law—usually, a portion to the current spouse and the rest to be equally divided by all living children.
It is important to know if he has completed any legal docs (Durable Power of Attorney, Healthcare surrogate or healthcare POA) and if so, who he has designated (and hopefully he doesn't have old docs designating a previous spouse). If he wishes to have you all involved in decision making, that needs to be documented properly in these legal docs. It starts with having a conversation with him--and take a sensitive approach so it doesn't sound as if you are not trusting of his spouse, try to create a positive spirit so things don't unravel.
If he doesn't have the documents in place and becomes incapacitated, the family may end up going through the process of guardianship. In some states, there are also healthcare proxy laws (I'm only familiar with FL on this--but in FL, there is a "natural progression" of who is looked to for healthcare decisions if no documents are in place: spouse is first after an apppointed guardian).
It's good to be considering this now: start the conversation, then hopefully he can put his wishes in writing. A good elder law attorney can assist with this. There are elder mediators and geriatric care managers trained in working through these discussion and conflicts, if you need additional help as well.