Tricky.
I had a friend whose mother died when we were 15 - her father waited a fairly short time before moving in the woman he'd had an affair with, whom he and his wife had nearly split up over, and her daughter, who may or may not have been my friend's half sister, it wasn't clear.
It made her extremely angry (obviously) and she left home as soon as she was able.
I had another friend, whose father left the mother for an OW - he managed to forgive his father, despite being very much a "mother's boy", but his sister never did, because she was as "daddy's girl" and felt as much betrayed as her mother did. She hasn't seen him for years.
So the wounds run very deep and it can be very hard to forgive - up to the person individually. You've managed it, but there is no guarantee your sibling will, and nothing you can do or say is likely to influence it.
However, it needs to be cleared up. Your father can't hide this situation forever; he is entitled to have someone in his life if he chooses, even though it's rather poor taste to pick someone who was a cause of upset to his wife before she died - but he can't control how your sibling will react, and tbf, he may just have to take it on the chin if they go off the wall about it.
As to the money - that's really irrelevant. If your sibling really needs that financial support, then they either have to subjugate their feelings about your father's revived relationship, or find another way to get the funds. Either way, not your problem.
Your only problem is that you are likely to be tarred with the same brush as your father when your sibling finds out that you've been in on the secret and not told them.
So between you, you need to get it sorted soon, and hope that your sibling decides to forgive.