Second marriages require special planning. There are a lot of things that need to be addressed to avoid problems. First, the spouse is not your kid's mom or dad. So where will dad be buried when he dies? What about medical directives and things like power of attorney … who is in control as we age and stop functioning in the way we used to? This requires a lot of planning to address the issues before they get to a critical stage.
Everyone is right and everyone is wrong! I understand that the kids want to see their dad and make sure he is OK. I understand that the wife has problems with his family and would rather avoid them. She is his spouse, who he chose when he was coherent, and they are the kids who have been around with him for their entire lives. These conversations are extremely emotional, generally not rational and can create even greater tensions as the situation continues.
It's always about money, even if it isn't. Estate planning, especially in a second marriage, can require a lot of thought and effort. Does everything go to the surviving spouse, does it get split with the kids, does it go to the wife first, and what's left goes to the kids? If it goes to the spouse directly, the kids generally see that as you just stole from them. If it goes to the spouse first, then what is left over goes to them, then every dollar she spends is seen as taking money directly out of out their pockets, slowly, for the rest of her life. Either way, there is a lot of tension that does not get better over time. Even if the kids do not care about money, they care that the spouse (who is not their mom) is getting it.