Welcome to the forum. This is a good place to talk about mental illness in general as well as your specific difficulties.
Our interpersonal skills can be upsetting when both people believe they know all there is to know and act on that belief. I can see how frustrating this must be. I was imagining my dad in a similar situation and I believe he would also have dismissed any of "that rubbish about mental illness" despite being a very caring person. But then our respective dads were brought up in a different time and absorbed the beliefs of their generation. Sadly the attitude towards mental illness was to believe it was shameful, should never be mentioned and to insist friends and family should "Man up" and get over it.
I am pleased that this is not such a widespread attitude today though it's still a difficult topic to discuss in public. Many people are afraid of MI, have no idea what to say to anyone with a MI and get very embarrassed. I believe this will change but it will be a slow process. Pretty much like your journey at the moment.
It's hard to find you have become anxious again when you thought you were getting on top of it. It doesn't take much to set us off at times no matter how much we believe we have systems in place. One of the most difficult things is I’ve also been trying really hard to love myself. I'm not sure how you do this. Perhaps it's more being able to accept ourselves as we are. After all, this is the attitude couples have towards each other.
If you feel it is impossible to talk to your dad do you think it would help to seek some professional help? Can you go to the person you saw 4-5 years ago? Have a chat with your GP and see what is available. It may help you to be more gentle with your dad and more helpful for you. I know when I am annoyed with someone or something it takes a lot of energy. The less energy we have the more it seems important to remain angry. Well that has been my experience.
Do you think you can have a chat with your dad? Perhaps ask him if he will listen to you while tell him what's going on and invite him to explain what he believes. You can say upfront that you are not trying to tell him he is wrong or change his beliefs. Simply an exchange of thoughts may help you both.
Hope this helps. Please continue to write in here if you find it useful.