Sure they could; parents make decisions about their children’s upbringing all the time, and if they don’t, they are bad parents.
What I’m saying here is that if you believe baptism to be salvific, only the person being baptized can make that decision. Infants cannot. You guys make up your own rules as you go along.
We’re talking here about baptism as you believe it to be, salvific. A parent doesn’t make a decision for a child as to whether or not they are saved. Baptism/Dedication, fine, but neither is salvific. Only YOU, as a person, can decide whether or not you want Christ.