The stylus I am using doesn't write well, Could this be because of the screen protector, or the app? Can I use the otterbox defender case without the screen protector?
Yes, it could be the combination of the stylus and screen protector not playing nice together... you can try removing the screen protector... or, different styli until you find one that works with the screen protector.
I have an Otterbox Defender on my iPhone and never had a stylus issue. I even made a crude stylus with mechanical pencil, a paper clip, and a thumb tack. It worked great. But an iPad IDK!