It sounds like your mother needs to feel she is the "manager" and needs to have the control of things. If that is threatened in any way she withdraws in anger. This developed a long time ago in her and isn't anything you can change about her. Her not being able to buy that lot was about her wanting control over it, when you chose to buy it yourself, she could not handle that and withdrew. What you did not see as a problem was to her a problem. That's how she was when you were younger too, so as you can see, that never changed in her.

You will probably outlive your mother, and eventually will own two lots that ajoin each other. In the meantime, however, your mother will probably continue to withdraw anytime she isn't given full control. You are willing to share, she can't be that way and never could be that way.