Er, she didn't vanquish Queen Chrysalis. Shining Armour and Princess Cadance did, with the power of love. :3
Also, continuing from the other content of the original post, Celestia didn't ask her royal family because:
1. Twilight Sparkle and her friends bear the most powerful things in Equestria, the Elements of Harmony.
2. It isn't shown or said how big her family is.
3. Her family may not be as powerful as the Element Bearers.
Also, I really doubt you can become an Alicorn. If that was possible, unicorns with great magic ability would be becoming Alicorns and proclaiming themselves royalty.