I hope you don't mind but a few more thoughts from me,
Although it was a few years ago I met Kerry we clicked very quickly and I would have described her as a close friend within a few weeks. I was then in my 60s whilst she was in her 20s
I agree that age gaps shouldn't matter in friendships but I was aware early on that my children would naturally feel threatened by me having a close friendship with someone who was nearer their age than mine so I have kept the friendship and family in two separate boxes. That could be viewed as me being secretive about my friendship
Knowing Kerry's life story and knowing she didn't have the same opportunities and advantages my children had growing up I have helped her financially and did that fairly early on in our friendship. She never asked for it and I always had to insist but it was something I wanted to do. If my children knew I imagine they might conclude that I'd been manipulated in some way or maybe they'd be angry with me.
I agree your father has been incredibly insensitive. Yes everyone male and female should always put their existing families first but maybe your father thinks you have grown up just fine and you don't need him any more? You don't need to read many posts on Mumsnet to realise how many men don't prioritise their families if when they still have young children. I'm certainly nor saying it's right but sadly it is the case for many fathers.
I'm guessing throwing the remote shows your father is upset by the conflict although I don't think it's the best way to show you how much he cares.
You say, "The issue isn’t him having a new friend, it’s that his friendship is at the expense of his family. No matter his new friends age, or gender. If he was hanging out with a group of guys playing golf, we’d still be feeling sidelined and hurt by his prioritisation of the golf lads." I can understand that but it shows it's not just about his choice of friend.
From what you have written the scenario as I see it is something like this,
Your father is retired and has lots of time on his hands and your mother isn't able to share his hobbies and interests as she is tied up with caring responsibilities whilst his children and grandchildren have grown up and have got their own lives. He has met a young girl who isn't particularly mature but she shares his interests. She is genuinely interested and will listen for hours whilst he discusses his car and his training in the gym. Granted putting her on the insurance was again insensitive but I assume he would say that you've never expressed an interest in his car or appreciate how high spec it is. That's not a criticism of you, my eyes always glaze over within minutes when men want an in depth discussion about their car.
Anyway your father obviously gets a lot from Tracey and to his credit he hasn't been secretive about her. He has also involved your mother in this friendship which I feel is important.
I guess you all need to work through how he can balance his friendship with Tracey with the families feelings of being sidelined.
Of course I could be completely wrong and Tracey is actually a psychopathic manipulative killer from a Net flicks drama.
I genuinely wish you all luck in getting through this.