Firstly, a pathological liar is someone who actually believes what they are saying..
Secondly, your sister didn't "make you" buy those things. You did it in the hope that she would show you more love and appreciation than she has.
She seems to be the type, from what you write, that feels inferior to you, and thinks that the only way to be better is to drag you down, rather than raising herself up.
Now you're trying to make nice again by having her participate in your wedding, even as she tries to poison your relationship with your mother?
You're going to have to stand up for yourself at one time or another. I hope you have a written agreement on that money you loaned them. Personally, I'd give her an absolute deadline on when to start repayment of that debt, and if they don't, then take them to court.
If you're going to be married, you need to be a grown up. People can only take advantage of you if you let them.