Hi -
The best thing you can do for this puppy is just think of it as a puppy, not as some special "prince/princess" type. There isn't anything more "princessy" about this mix of breeds than any other dog. Most of what a dog eventually becomes is based on how it's handled. If you WANT your dog to be like a princess, you could do that by treating it like a princess all the time - but you'd probably end up with a problem dog.
We see a lot of little dogs that act spoiled because people tend to spoil them - they're tiny, they're cute, and they get away with things that a big dog wouldn't. But when it comes right down to it, they are all just dogs.
Get her into a good puppy kindergarten, teach her obedience, try not to coddle her too much, feed her good food and make her have manners (so many little dogs don't, but that's 100% a TRAINING error not something inherent in little dogs).
By the way, the mix of those two breeds would just be a mixed breed, not a hybrid. I'm sure she's really cute!
Melanie and the gang in Alaska