A lot of times when you ask a professor to change your grade like that, they’ll come at you with a question like, “Why didn’t you come to me before final grades were in?” I would try to think of a reason for that. Were you in office hours a lot or did you rely more on the tutoring sessions? If not, they might ask why you weren’t. If you were, they might ask why you didn’t talk about withdrawing before the final grades were in.
(I’m also concerned that it may actually be too late to change the grade. If it’s been sent to the Registrar’s office, the professor may not be able to apply a curve or change the grade at this point. That might be something worth checking because it would be a shame for this to screw you up.)
When you’re working on your appeal (I would recommend getting that process started as soon as possible, regardless of whether or not you send this letter out), I would try to construct a scenario for how you can do better in the future. Engineering classes probably get harder, not easier. In addition to tutoring I would definitely talk about things like office hours, extra time spent, maybe joining a study group or study hall to ensure that you’re not in this position again. It’ll be tough if you were already on probation but I would recommend trying.
I hope this works out for you. Engineering can be tough and I really admire your passion for the subject. Not everyone is cut out for it (I know I’m not!) but if you can find some way to hang on and develop new strategies for moving forward.