I'm guessing that ultimately it's less about the house and the "money" than it is to do with him moving on so quickly, being with a woman who clearly wants him to have less to do with his own children and more to do with hers - this has happened to a friend with his father and the new woman in his life, it's all about her children, he hardly sees his father, despite him and his wife having him live with them for a long period after my friend's mum died. He's pretty much been dumped and it hurts.
Unfortunately, there is so little you can do about it. I'm glad that you have a sister, so that there is someone you can hold on to and share this added grief with. I'm all for those who are widowed moving on, but this does seem a remarkably quick thing and that can't not be hurtful to you and your sister.
I had a similar, but mostly quite difficult thing happen to me with my stepfather. There was no money involved at all, but ... well he had been seeing a woman for a number of years - I'm assuming they're still together - many years after my mum died. I love/d my stepfather very much indeed. My own father died when I was ten and there were many difficult and horrible years before my mum met and married him when I was nineteen. He adored my mum, almost worshiped her, and he fell apart when she died. He'd always been a drinker but became a full on alcoholic. Luckily, at some point, he realised that this was not the way to go and not what my mum/his wife would have wanted. He stopped drinking, read more, went back to school, turned his life around and it was wonderful to see. I was so proud of him. Then he started seeing a woman who was difficult. That's an understatement. He'd seen a couple of women previously, one who I really got on with and hoped that they'd settle down. [n.b. I wanted him to find love, I urged him to date and find someone else he could love and share his life with]. The difficult woman is an alcoholic and my stepdad seems to have taken it upon himself to rescue her. They have split up at times, she has tried to burn his house down, broken down his front door, once she went to the police and accused him of raping her and he spent a night in jail, before she recanted and told them she'd been trying to punish him for not wanting to be with her. And on, and on, on. I never once said "You must leave her!" But I did tell him how worried it made me and that he couldn't rescue everyone and that maybe there was no way she could ever be "fixed", but he'd get back with her and I'd support him, with provisos. I never bad mouthed her. Etc.
I was seriously ill six years ago (at the time friends could not contact my father as he was staying with this woman's kids, which none of us knew), so he wasn't around while I was in hospital for a month and that was fine, a bit hurtful, but fine. I left hospital in the September of that year and was still very vulnerable in many ways when I came out, but working to pull my life together. All was fine with him and me. We spoke, we had long chats about religion and politics and blah. It was great. Then in the December, in the run up to the jolly joys of Christmas (yes, sarcasm), the woman got hold of my phone number and started phoning up and abusing me. I'm talking full on abuse, saying things that were beyond vile. Bad things happened to me when I was young with men. She said I'd loved it all, wanted it all, was a dirty slag, just like my mother, who was a prostitute, I wanted to have sex with my stepfather and that's why I was trying to push her out of his life. And more. I stopped taking the calls but recorded the voicemail messages she would leave. I told stepfather, he was horrified. I told him that I wanted to contact the police and he said I should. So I did, they listened and were pretty taken aback and she was served a severe warning - she was well known to the police in the area she and my stepfather lived in - and that if she did anything again, she'd be imprisoned. So the calls stopped, the threats to come to my house and burn it to the ground stopped. And then, at the beginning of the year, just after new year, I spoke to my stepfather and he told me that him talking to me made her angry and that he was sorry, but he could no longer be in touch with me. The end.
That was over five years ago and it still hurts. I don't think about it most of the time, but when it comes into my mind I feel as though I've been punched in the stomach all over again.
Sorry! This doesn't help. I guess, well I have no idea what got into my stepfather and no idea what's gotten in to your father. I think with my stepfather it's that he's a week man who wants to make all people happy at all times, but can't, so ends up seriously hurting one person. Maybe it's similar with your dad. He can't bear to be alone and is prepared to make his own children unhappy in return for a comfortable life for himself? Whatever it is, I'm so sorry that you have to go through this so soon after your mother has died. I hope that there is a way of dealing with this that doesn't get so awful that you're hurt even more.