I decided to go to a sewing group I am a part of, and asked their opinion. I was told to get a stretch needle or a microtex needle. I rushed to Joann's, they were completely out of stretch needles, but they did happen to have a microtex one. Which they should - considering some of the crazy Halloween fabrics they carry.
What a difference that needle made. I could not believe how smooth the rest of the sewing went.
The vintage pattern, dating 1976, was super easy to follow. But, the top happened to be too big and the bottoms too small. I altered the bottoms, and just tied the top around twice. Fits just fine now. Lil' Miss loves her new suit, and wants to wear it all the time. A direct quote: "I always wanted an Ariel swimsuit like this. It's my favorite! Thanks mom, for making it for me." Ahh, sweet and polite.
Literally has been wearing it every time we go swimming. She doesn't want to model it for me, so this is the best picture I got.