How do I calm her down? I have no clue!?

I'm still a novice rider but not a complete beginner and my horse/pony. I believe she is a pony at measuring 14.1/14.2hh. She loves to jump because that's what she specializes in. Recently, she has being getting quite whizzy, especially with another horse in the arena, so I'm trying to avoid that. I'm gonna try some exercises to try and stop her from guessing what she's gonna do and just wait for my command. She knows exactly what she's got to do she was show pony and knows how it's done but she has now started to after a jump bring he head down when landed and what I believe she's trying to do it grab the reins out of my hand, it gets difficult to guide her where to gow when she does it. I like her enthusiasm to work but I do want her to concentrate alot more. I mostly blame myself because I don't know what the actual problem is. She wears a flash, martingale. How can i correct her when she does the pulling thing? Once i asked for a trot (with another horse in the arena) she cantered around insanely and took me a while to stop her. (i wasn't telling her to stop correctly) I'm still learning. So basically, does anyone no some tips and expeshially some exercises to do in arena and change up the same old boring work we do. I need to get more confident in my jumping because I have a jumping pony who loves to jump and I'm still lacking guts when it comes to jumping but I will jump but I want to practice cantering, trotting, being in control first. Thankyou!