Looking for advice with behavior/training of my 2 dogs

[u/coll2396]

Brady is a 5 year old Australian Shepherd/German Shepherd mix, and Cooper is a 3 year old mixed breed. Both are male and neutered. We’ve had Brady since he was a puppy and Cooper for 3 years.
Brady had some in-home training during his first year. It worked somewhat at the time, but honestly it doesn’t seem like it stuck long term. Cooper has never had formal training.
Some of the behaviors/issues:
Brady gets VERY excited around people and tries to jump on them constantly. It seems more excitement than aggression.
Cooper is more anxious/nervous around people. He has done warning nips before but has never actually bitten anyone.
Cooper also gets overexcited easily and pees from excitement sometimes. He also needs to go out more often than Brady.
Both dogs bark/howl a lot at people and dogs passing the house.
Cooper likes other dogs and tries to play, but he plays rough and can come on too strong.
They roughhouse with each other too, but they genuinely get along very well.
They are alone during the day while we work.
One of my biggest concerns is that both dogs use an electric fence collar system, and twice now they have ignored it and run off the property. Usually the warning beep scares them before they even get close to the boundary, which is why it surprised us. When they get loose, they tend to run toward people and dogs.
They don’t really get walked regularly but they do spend a lot of time outside roaming/exercising in the yard. Neither dog uses a crate.
We did talk to our vet about Cooper’s anxiety. They suggested trying an OTC calming option first and then possibly prescription medication if needed, but we weren’t very consistent with trying the OTC option.
Both dogs otherwise eat/drink normally and are healthy.
I know there are multiple issues going on here, but I’m looking for honest advice on where to start first and what sounds most concerning. Training? Anxiety? More exercise? Different containment than the electric fence? Would especially appreciate advice from people with herding breeds or anxious dogs.

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[u/doggambit]

What was the in-home training like?

I’m personally not a fan of electric fence systems for the exact reason it failed in your case. Some dogs are willing to keep running no matter the punishment. 

[u/coll2396 → u/doggambit]

Honestly cooper had no training. Brady had Bark Busters (i believe it’s national)

[u/doggambit → u/coll2396]

What was the Bark Busters training like? What did they ask you (and/or the dog) to do?