We still don't have enough data on whether this will suffer ADE. If parent is young, isn't in a highly infectious area and behaves cautiously, they may be making a less risky decision.
We absolutely have enough data to rule out meaningful ADE. Study after study (the phase 3 trials and all the ongoing surveillance) indicates a massive reduction in the rate of severe infection among vaccine recipients.
Sure, one can quibble about whether maybe some of the very small number of people who got a vaccine more than a couple weeks before a severe COVID case had a form of ADE, but that’s like saying that we haven’t ruled out that seatbelts might kill people. In both cases, the risk that a protective measure harms the recipient is massively outweighed by the degree to which the protective measure protects the recipient.
By that standard, you also can’t rule out disease-induced ADE, dengue style.
But the vaccine developers do know what they’re doing. IIRC, with SARS, a lot of research was done that suggested that antibodies against N might cause ADE but antibodies against S would not. If that carries over to COVID, then maybe one is better off with a vaccine than natural disease: the latter induces antibodies against N but the former does not.
Very few reactions have occurred. If you're worried about it, also don't go outside, cross a street, or go swimming in any body of water.