Hi Kendrick, and welcome to the forum!
What Mercedes is doing isn't weird at all - at the tender age of six months, she is trying to control you.
Welcome to the world of GSDs! At six months it is not full-blown dominance, but she is not showing appropriate submission to you, as the pack leader, for her age.
She wants to be petted when SHE decides, not when you decide, thus the ducking of the head when you reach to pet her, and then pushing into your hand (taking control).
She is still very young and sounds like she has a wonderful temperament being so sweet and gentle with your two year old. I commend you for wanting to deepen your bond and build your relationship with Mercedes, and the very BEST two things you can do to start off on the right foot and to continue in the right direction is:
Start implementing Nothing In Life Is Free (NILIF) right away, and sign up for some positive/reward based group obedience classes. Oh, and forget about the training videos - nothing earth-shattering about this "method", other than a good way for the author to make a living.
Google NILIF for more info. It is basically a basic life-style for you and your dog where in everyday non-threatening interactions, your position as alpha and benevolent pack leader is subtly and directly implemented and continually re-inforced. It is simply asking the dog to work for everything. Food. A toy, Attention. Going out. Sometimes all you really ask for is a sit, eye-contact, waiting a few seconds - not much, but the dog is defering to you and waiting on you for permission for everything.
Training: Going to classes WITH Mercedes will do wonders for your bond and relationship. Training the dog is just a small part of it. Training the trainer (you!) is the big part of it. That is why it is very important to go together. A good teacher can be invaluable at watching you and Mercedes interact and give help and feedback. A six to eight week course is very affordable and will get you started on getting Mercedes where you want her. Training is an on-going process, because dogs forget if their training isn't maintained and refreshed on a daily basis. Years ago I used to think that training classes were a waste of money, but gave up and signed up when I was having problems with my rescue. Well, did I learn a lot!!! It completely changed my understanding of dogs, completely changed my relationship with Keeta for the better, and turned her behaviour and attitude 180 degrees around! Plus, added bonus, it was fun! I just couldn't stop, and went on to more advanced classes, and I am still hooked on training and working with my dogs.
So to sum up:
Mercedes sounds awesome!
Google NILIF and start implementing right away.
Find some classes and sign up, and most important,