Ah, the eternal dilemma: to snip or not to snip. We feel this one in our bones, and in our feathers, if we had any. Here is a young chicken keeper, clearly devoted to their flock, facing off against a mom who has simply had it with the "poop everywhere" situation. We get it. We really do. A homestead is a place of compromise, and sometimes that compromise involves a pair of scissors and a very grumpy hen.
The good news is that you are not wrong to be worried. Wing clipping is a practical solution for containment, but it is not a cosmetic procedure. It removes a chicken's ability to escape ground predators, to reach high roosts, and to feel that fundamental sense of freedom that comes from a good, clumsy glide. Your flock is already showing signs of stress from overcrowding, that 20x5-foot area was a recipe for unhappy birds. They are getting out of the new 1/3-acre pen because they are smart, and because chickens, even gliders, will find a way to explore. A clipped wing does not hurt them, but it does change their world. It makes them vulnerable in ways they do not understand.
So, what can you do instead? First, look at the fence. Chickens are escape artists, not aviators. If they are flying over, that fence is too short or too inviting. A simple addition of a few feet of bird netting or a lean-in at the top can stop a determined flapper without taking away their wings. Second, talk to your mom about enrichment. A bored chicken is a chicken that plots escape. Give them things to scratch, peck, and explore inside the pen, a dust bath area, some perches, maybe a hanging cabbage. Happy chickens tend to stay put, because the grass is not actually greener on the other side; it is just slightly more poopy. You have a good setup already. Do not let a temporary frustration lead to a permanent change you will both regret. The roosters may be tanks, but a clipped bird is a target, and a clipped bird is a sad bird. Protect their wings, and find a fence-based solution. That is our honest, poop-stained take.