Thanks for sharing this! Unfortunately, though, it seems your argument is invalid in its form.
You claim that premise 3 of the argument follows from premises 1 and 2 by means of modus ponens, but this is not the case. In premise 1 you offer a conditional, and instead of affirming the antecedent, as a modus ponens argument would, you instead affirm the consequent, rendering the inference from premises 1 and 2 to premise 3 invalid. This is because the premises of an argument that include a conditional and then affirms the consequent could be true, but the conclusion of the argument could still be false (e.g. 1. if you live New York, then you live in the U.S. 2. You live in the U.S. 3. So, you live in New York).
Maybe you just accidentally switched up the antecedent and the consequent, which could be fixed and could give the argument its validity in form. Instead, premise one could be put like this:
1. If we are held responsible for our decisions, then our decisions are not influenced through intervention by God.
This would allow the rest of the argument to follow validly and not undermine how you ultimately reach your conclusion instead.
As far as the soundness of the argument, separate from the validity of its form, I think premise 4 to be a false premise. First, by "influenced," I take it that you mean "overridden" based on what you wrote above before laying out the argument, so that is what I will mean when I use "influenced."
It seems, to me, that petitionary prayer could be useful without our
decisions having to be influenced by God's intervention. It certainly seems plausible that our ability to make free decisions could remain intact while God intervenes in response to a petitionary prayer. I do not see how an answered petitionary prayer, such as someone who is sick and asks for healing is this healed by God (this is also an instance of where petitionary prayer is useful), would entail that this person's free will, i.e. the decisions they make, is being overridden. Because of this, I think premise 4 to be false.
In summary, this argument is invalid because of its form. However, if the form was fixed, I still think it to be false in light of the objection I rose to premise 4 of the argument.