Now, this is belaboring the issue, sorry.
While there is no "magic formula" in the Act of Contrition, we shouldn't adlib either, or then it becomes a novelty. The words in the Act are tried and true and that is the reason we are required to memorize and recite them. Isn't this the way we have been taught in preparation for First Confession and First Holy Communion. Why bother with memorizing when our interior disposition is sufficient? Is that what is taught in the RCIA? When we start changing words to our own liking and think it is okay, we will end up left to our own devises and be led away from what is the true form of prayer, the rule of faith. Can the Apostles' Creed, the Our Father, the Hail Mary, the holy Rosary, etc., really be reinterpreted in our own words and convey the same meaning? I don't think anybody can improve on these prayers. For that matter why do we flay and excoriate against the reformers of Vatican II for "improving" and reconstructing the holy Catholic faith, the form of prayer (the Mass) and then end up saying nothing is wrong with the manner in which the Sacrament of Penance is performed if not followed to the rule? What if the priest doesn't use the correct formula of absolution and uses his own words, is the sacrament valid? [Yes, it is valid because we are protected by the principle of "common error"] But if we insist in saying the Act of Contrition is not essential to Confession, and will not invalidate the Sacrament, that's a novelty worthy of a novus ordite (such as the priest who ordered the little girl to go and cut short her recitation of the Act). It is true that interior contrition is sufficent, but nonetheless it is required to be recited when the priest asks so. I know a few Catholics who have been away from the Church for many years and go to confession as though the first time. One fellow told me he had forgotten the Act of Contrition and told the priest, who led him through the prayers and then gave absolution.The shortest act of Perfect Contrition is, "O My God, I am heartily sorry for having offended Thee because I love Thee." This remits sin immediately (with the intention of going to confession ASAP), and is best to say at the moment of imminent death. Now, this is a formula prayer (a concise form of the longer one but has the same intention) and would be sufficient to say in confession, but is it what the priest expects? I'll try this the next time I go and see what the priest comments or reacts.
Anyway, for the children making their first confession, it is understandable that they may stumble on the words and it's not a big deal. I am talking about adults who are steeped in the Faith and who should know better. I'm not going to go around teaching whoever (especially new converts) not to worry about not reciting the Act of Contrition as it won't invalidate the sacrament. It's not how I have been taught. It's not how the Church teaches.