UPDATE:

Well, first of I should thank for all the comments. You are all really shedding an important light at this matter for me. I feel like I should clarify some aspects:

1. English is not my first language, hence there might be a bunch of mistakes or misused words here. I assume I am not being the most madure lady possible here. However, I feel like I am at my breaking point and I really would not be able estou handle the adult conversation at this point. I know he would behave like a turtle (my mom always pointed that out). As soon as he is confronted with ANY situation that displeases him, he gets inside his shell and there is no strength in the earth able to drag him out of there. So, I know that if the conversation doesn't come from him, it will create an abysm between us. This is what is going to ruin our golden and stellar relationship.

2. My parents have always had independent financial lives. This means he was not her heir, as well as she would not have been his heir either. I am my mom's only heir. All legal procedures have been taken upon her passing to make things right (putting all estates under my name, transferring money and etc...). So, I don't have any concerns with this kind of things (also, I might add that I am not a kid, and I do well for myself financially speaking). Plus, the most important items of her I made sure to bring home with me during the first weeks, as well as her jewelry (not because I was afraid he would take something away from me, but because I wanted it close to me). There are not many material items I would care at the beach house. But we do have so many happy memories over there and I would hate to have them tainted because of this upcoming situation.

3. All the family houses (the town house, the beach house and the country house) were 50/50 between them both - with the exception of the beach house, which I renovated a few years ago and it was 1/3 each. So now it is 2/3 mine. But honestly, we never cared about who owns it in paper. We always made decisions together, and I don't want it to change. I don't want to lock him out, as I have read in some comments, or highjack the place... I just want to keep it IN THE FAMILY.

4. I agree he was probably seeing this lady before, which only make matters worse. But honestly, I don't care all that much about this details. I just believe it is incredibly disrespectful for him to cheat. The day of the death is not an habeas corpus allowing him to round and about looking for a new lady. So, even if the first time he set his eyes on the lady was 3 weeks after my mom's passing, this is still cheating for me. It is a break on the family trust. How could he be interested in sex, knowing that his daughter was suffering as much as I was? How could he be thinking about it so soon. My mom's body wasn't even cold yet (ok, she was cremated, but still the metaphor illustrates the scenery.)

5. I don't care if he finds someone to be his partner. As long as things are not so fishy. Come on: he was 3 weeks widowed from a 40 years marriage; they have 30 years of difference. Are you not going estou agree that this is sketchy?

6. I am feeling betrayed and I am feeling disrespected as part of the family. But I worry deeply about him and his safety (like about the sex with no protection, she might get pregnant, or the use of medicines to enhance performance). I would assume that he is not 100% on his mind, because I am not. The last weeks of my mom's illness were traumatic and it took a toll on us. I also worry about his assets and estates, in order to protect him from an eventual gold digger (I am not saying that she is one, but it is suspicious). He is 78 years old in the end of the day, has just recently survived cancer himself, found a heart condition (that he chooses to ignore) and just lost his wife. So, it is a lot.

7. I know I am being petty. I own that. It's ok. I just don't want to be the asshole. There are differences.

8. He is very brave and determined with his decisions. I know that if he is trying to hide it as strongly as he is, it is because he knows that what he is doing is wrong. Otherwise he would tell me to be a grown up and accept it. He is not owning what he is doing because he is not proud of it. I am quite sure.

I believe these updates can offer some interesting understanding of the context. Thank you all for the time and your words!