Convincing a stubborn mom...
One thing that worked for me most of the time was to write a letter to my mom (also the mega boss), where I would tell her about how much I wanted something, the things that were involved in owning it, how I would be responsible about it and how it would affect her life (I made sure to list all pros and cons from her perspective, so I would show I had done my research and took into account her feelings (important in negotiations with mom)). Writing a letter guaranteed that she would read it, otherwise she didn't hear me out, and would slam down the idea on my first few words.
This is what I would suggest you do: since you have your dad's approval, enlist his help to write the letter. Be sure the letter is well written with no grammar or spelling mistakes (have friends, teachers and/or your dad proof read it). She must have told you why she doesn't want you to have a snake, so you can explain the reasons that would appease her reluctance. Verify with your dad that you have gotten all her reasons right, and that your counterarguments would be effective. You might also have to work at it to lay down the basis for your arguments before you write the letter. For example, if she doesn't let you have a corn because your grades or behavior aren't to her satisfaction, you would have to work hard at being a model student before you even mention anything about snakes, and to prove yourself can take a few months. However, if your mom is simply afraid of snakes and would otherwise let you have one, then you must reassure her in your letter that the snake is not going to escape and how you can guarantee that, etc., and how this would be an innocuous opportunity for her to overcome her fears. If it's the financial aspect that stops her, then present her with a plan on how much it would cost and how you'll finance it (you might have to take a summer job to prove it to her).
Tell us about her arguments against you having a corn (be honest) and we can help you come up with solutions.
All this being said, your mom might still say no, and you might still have to wait a while before getting your corn.