Not sure what to do

[OldFool]

I'd have to agree with much of what Just_Me said. As for the Newcomers section, it's certainly fine, but I'd disagree that you won't get good responses elsewhere. More specific forums such as this one don't have the flurry of activity, but in general, the folks you'll find (IMHO) have more experience.

However, my only solution (since I didn't talk about this problem with anyone, including XW) was to have a kid (something that neither of us previously wanted). That really upset her, as she saw a child as ending her life as she knew it.

Dang...not a great move. I'm hoping you now realize that children never solve the problems in a M (why is it so many people think that?!?) You didn't have one, did you?

As she was leaving, I went out to her car to ask her a question and saw some plans on her passenger seat for a kitchen island, plus a tape measure. She had said something last week about the mortgage being in her name still (she found out through running a credit check), so I jokingly asked her if she was buying a house.

OK. Well we all know this wasn't a "joke" or even funny for that matter. You wanted to know what she was doing and just couldn't let it ride so, knowing full well that a direct question would most likely elicit a "none of your &#@*$ business", you asked "jokingly". Can you spell t-r-a-n-s-p-a-r-e-n-t? We see it...so did she. This is just one case and that's not enough to do any damage, but if it is part of a pattern of behavior on your part (and I'd guess it is), then it's an issue and has likely continued to push her away from you.

My question is how can I start a relationship with her again, even one just talking, if she won't let me in?

As Just_Me said so succinctly, you can't. So stop trying. Let her go for now. There is absolutely nothing you can do (yes, I know that is frustrating) and attempts to engage her or find out what she's doing appear to be met with less than impressive results. So as Michele says, stop going down those cheeseless tunnels.

I realize I scared her last summer, and I have apologized profusely and repeatedly.

I'm not sure what this is all about, but I'd guess it's not too good. If you've apologized once (sincerely), let it go and don't apologize again. Apologies are fine, but they're just words and that only works for minor infractions. Big issues need action (or, sometimes, inaction).

I'm racking my brain trying to find out ways to just talk to her....

Well, stop. She's an adult. When she's ready to talk to you, she will. Until then, cooking up "ways to just talk to her" will be counter-productive.