Q: Dad can't care for mom alone anymore, but refuses to put her in assisted living. Can we intervene?
I'm not sure that you can convince him. What you can do is to spend some time assessing the situation regarding your mom. You also have to assess what caring for your mother is doing physically to your father. Is he able to do this very challenging job? Is he able to emotionally handle it and is she getting the best possible care from him?
Since this is your father we're talking about here, you will need to approach him in a way that he'll understand and relate to. In other words, how does he handle conversations? Women tend to approach these subjects from a more emotional place, but if your dad doesn't do that, then you will need to tailor the conversation so that he can relate to it: state the facts. It's not easy, but understanding your father's personality is key to the success of your conversation with him.
There is also the issue of guilt. You can see the benefit for your mother and your father that an assisted living facility would provide, but years of living together and caring for one another makes separation a very difficult and emotional decision.
If you are going to have the conversation, be sure that you have done your research about the facilities you think would best serve your mother. You will need to make sure that your father knows he can be with your mother whenever he wants and that he will be part of making the decision on where to place her.
Finances are another issue. Be certain that your father will be able to afford to pay the facility. If finances are an issue, he might very well be frightened and too proud to discuss this with you. If he doesn't already have caregivers to help him, this is often a good place to begin.
This is a journey, and it's full of twists and turns. Sometimes you have to take small steps and be patient. Before you have the talk with your dad, be sure you've covered all your bases and that you have clearly defined answers and solutions for him. You must do this in a kind and loving way.