Why would the discussion of him buying a house have come up? I thought you were going to back down from the R discussions. You have got to get control of this.
Is he lying to you? Absolutely. Is your tracking of his vehicle causing you to cycle and act out in ways that are detrimental to your marriage? Absolutely. Please stop keeping tabs on him and stop your endless list of his lies. Let his life be a mystery to you and let yours be a mystery to him.
We've all been telling you to live as though he is gone so that you can detach and move forward in a way that will give him space and you peace. But you are refusing to do it. You wake up each day ready for a new round. I know you'll say this is just venting and you are being sweet in person, but I find that very hard to believe. Your hostility, anger, emotion, etc. have got to be coming across.
TO, please stop pushing him further away because you keep telling us that you want your marriage to survive. Please go back and read the beginners materials in the books and the links because you are not following the process and you are escalating your situation at every turn instead of de-escalating it as you should be.
Everyone here cares about you and your kids and wants this to work. But you have got to stop.