It's pretty clear what happened isn't it?
Meghan did not want, and does not want her batshit sister in her life. They have not seen each since 2008.
She was probably worried that if Thomas met Harry, he could not be trusted not to blab to Samantha who by then was in the press every other day talking about her.
I think she believed that she could contain the interaction between Thomas and Harry to just the wedding, but even that, Samantha managed to fuck up for her with that asinine pap photo stunt. Then when the rift grew between Meghan and her father, Samantha encouraged him to make it all public, which obviously made mending things difficult. He then started to blackmail her through the press, and was used by people like Dan Wootton and Piers Morgan who have an axe to grind with Meghan.
Add to that, Thomas then began to appear on conspiracy blogs that speculate on Meghan's children, and on which Samantha is a regular guest, and you can understand why Meghan can't trust her father.
He has chosen his two other children over her.
And that's his right.
She has chosen to walk away.
Which is her right.