Let me give you the point of view of a widow.
Depression is a natural and normal part of grief. For the first year your Dad struggled through this and whilst you (very admirably) visited every weekend, Mon to Fri he was alone in a house full of memories and reminders that his present and future life was changed forever, as was he.
You yourself know that the weekend visits were not good for your life, your marriage or your mental health, he would have known that too. So he pulled himself out of depression and away from the path of alcoholism probably for you, his child, and because of you.
At some point he met someone who made his present more enjoyable and made the future look worth staying alive for, someone who spent time with him not out of duty or pity but because they enjoyed his company. He then didn’t need to pressure you to visit so often and that was good for BOTH of you, and both of your mental health. You should be happy about that.
In more practical measures, your dad has made changes to the family home, but quite frankly in the last five years who hasn’t done a bit of DIY? Covid and post-Covid time saw a massive boom in house renovations and repairs. Your Dad shouldn’t have to keep his house as a shrine to his dead wife to appease anyone, it’s a home that he has to live in, he needs to be comfortable, physically and mentally there every day and yes, sometimes that means having a big clear out.
If your mum was still alive, and your mum and dad chose to sell their current home and buy a different one, would you expect to have a say in that? You may have an emotional attachment to the house you grew up in, that’s understandable, but a grown adult with their own money and (from what I gather) fully functioning mental capabilities has chosen to move house, most adult children don’t expect to have a say in where their parents choose to live.
So, in short, you’re sad that your dad’s focus is on his bride-to-be most of the time, but I’m willing to bet that more of your day-to-day time and energy is spent on your husband than your dad?
You’re sad that your dad is moving from the family home, but that could be the healthiest thing for him to do mentally; I nearly moved to a different country after my spouse died, I just NEEDED to be away from the constant reminders of the life I should have/could have had.
You’re worried about a potential loss of inheritance.
Well, life is short. You may die before your dad, your “inheritance” could be eaten up in care home fees, or if your dad had stayed sad and alone he may have spent it all on alcohol by now.
Surely you’d rather see him spend his own money in a way that makes him happy, rather than stay in his current home, changing nothing, doing nothing and drinking himself into oblivion?
By all means have a chat to your dad about your inheritance, but do try to be happy for him, his current life choices have probably saved your marriage and taken the burden of 8-hour round trip visits every weekend from your shoulders; that’s priceless. Enjoy the time with your husband instead of being sad about what your dad is spending his money on, you’re one of the lucky ones whose spouse is still alive.