I'm sorry, really I am, but I think you need to seriously rethink your run. It is only pure good fortune that you have not already lost most or all of your chickens, because it is MAJORLY not at ALL predator proof
Raccoons are excellent climbers. Also they are strong. They can climb over (or actually, probably just rip apart) your chickenwire fence in the blink of an eye. The wooden privacy fence is also very easily climbable. Seriously. We're talking maybe ten, twenty seconds to get over it. The 'front run' (last pic) is not at all secure either; if they don't rip the chickenwire apart, they will just climb up and over, going thru the unscreened gable part at the top.
First, you really oughta get something stronger than typical chickenwire. I would suggest at LEAST using 2x4" welded wire mesh.
Then you need either a full roof, or perimeter electric -- NOT atop the fence, but along the ground, preferably at least 2 strands, one at 4-5" (you will have to keep the grass and weeds well cut back so they don't ground it out) and another at 14-16". They need to be stood away from the wire run fence far enough that there is no question of shorting out in the wind or rain, and they need to be on a fully reliable charger whose strength is checked at least weekly if not daily.
(edited to add: the strength of an electric fence's "zap" is best measured in joules. You need something around 3,000 J (if I recall correctly) to reliably discourage raccoons - that is comparable to what you need for horses. You will need professional advice to choose an appropriate charger, because it depends very much on how much of what material you are running. DO NOT believe any of this 'charges X miles of fence' cr ap, as it is basically irrelevant to real world conditions. Talk to the customer service reps of major charger manufacturers or suppliers to get sensible advice.)
Catching and relocating raccoons is basically pointless (or anyhow is IN NO WAY a substitute for having a well built run) because there is a roughly infinite population of raccoons out there -- new ones will just move in -- and all it takes is one raccoon, once, to put a permanent and probably severe dent in your flock. Plus once they have et some chickens they will be much harder to keep out in the future. Best to prevent them ever getting a taste.
Barb wire would be pointless. It is meant to deter cattle and other large grazing stock. Several strands near ground level may *slightly* deter digging predators, but not enough to be a very good way of trying to achieve that goal around a chicken run (use a horizontal apron or buried vertical skirt of welded wire mesh instead).
Sorry, I know that's not what you prolly wanted to hear, but it's the truth.
Good luck,
Pat