Hi Gypsy,
First, I want to say, please don't be frightened of the color; black or white do not indicate it's nature/intentions. We see black, white and gray shades in between around here all the time.
Having said that, based on the information you've dug up, it could possibly be the previous homeowner that died there. S/he could simply be lost and think they still live there, and perhaps confused as to why there are 'strange people' (you all) in their house! It might sound silly, but it happens. This is why the home improvement projects seem to 'stir up' the activity. Whatever you're doing to the home interests them.
While the house blessings, etc. are good ideas, there is also a simple approach. Just verbalize (at any time) what you want. Just try not to do it when you're feeling scared yourself.. you need to be confident. Speak as you would to any other person; be firm, but be kind and polite. Tell them that you are now the homeowner and they need to realize this and move on. And to please stop showing themselves by walking around on the porch as they're scaring the kids. If they insist on staying, they are welcome to, but ONLY if they remain unseen and do not bother anyone.
I hope you find a workable solution!
Kell