We surprisingly don't have many squirrels in our neighborhood (mostly rabbits, which are less triggering for my guy), but I did let him off leash at a nearby empty park to chase the squirrels there once. He had the time of his life but his arousal was SO high that I honestly thought he was going to drive himself to a heart attack.
All that said, clearly my dog has a prey drive I'm not fulfilling so I'm going to try prey substitution training. He sometimes likes cat flirt toys, but loses interest quickly. This book seems highly recommended: Hunting Together by Simone Mueller.
what has the trainer recommended for the prey drive? predation substitute training is an awesome way to work with the natural prey drive and not fight against it
are there times where birds aren't active? eg: walking later at night
Here's a book that might interest you. I haven't been following it exactly, but I like some of her ideas for working with your dogs impulses and giving the appropriate outlets.
https://www.amazon.com/Hunting-Together-Harnessing-Motivation-Based-Substitute-ebook/dp/B085X18GMC
I usually start working on those issues with Look At That/Look And Dismiss (also called engage/disengage - I just learned it as LAT/LAD, so that's what I call it!).
Here's a good video on how to teach it, and how to use it when seeing those triggers: https://youtu.be/EdraNF2hcgA
What I really like about this technique (and make sure to prioritize getting to LAD over getting less distance!) is that it teaches the dog to self-dismiss those triggers.
I will say right now that you'll need more than just basic LAT for prey drive, but starting with it is going to be a great foundation. Later for critters, I like to do a lot of premack principle.
I haven't yet fully read the book (it's short, but I've got so many things on my to-read list!), but I've gotten through a good portion and watched several seminars by the author and I like Hunting Together by Simone Mueller. It takes the idea that dogs are naturally prey driven (in most cases) and it's good for them to be able to work on the predation sequence up to a certain point. You can also use portions of that predation sequence to reinforce paying attention to you, for example.
Check out predation substitute training (Hunting Together, Simone Mueller). Pattern games (Leslie McDevitt) are also really useful: 1,2,3,treat is my favourite because of how easy and effective it is for navigating by triggers.
Our lad used to have an absolute meltdown at any small animals, especially if they ran or behaved in a “fun” way. Now he can calmly watch, disengage, and keep walking :) he’s still got a super high prey drive don’t get me wrong, just more desirable (for humans) outward behaviours in response to it.
The most important step is preventing her from chasing in the first place. This probably means long lines and being pickier about where she's allowed off leash or when/where you walk. Chasing animals is extremely reinforcing so if she's allowed to chase then she's going to want to do it even more next time. There are a bunch of different methods, I use a combination of all three.
predation substitute training: https://www.amazon.com/Hunting-Together-Harnessing-Motivation-Based-Substitute-ebook/dp/B085X18GMC/ref=sr_1_1?crid=2BMG6OSHZ61BF&keywords=predation+substitute+training&qid=1643576664&sprefix=predation+sub%2Caps%2C135&sr=8-1
counter conditioning
https://pethelpful.com/dogs/Changing-Dog-Behavior-Through-LAT-Look-at-That
https://www.clickertraining.com/reducing-leash-reactivity-the-engage-disengage-game
game based training: https://absolute-dogs.com/products/chase
I know lots of dogs who have strong prey drives and honestly their owners don't do any training and just accept it. Their dogs are only on leash unless they're in fenced area, they use long lines, they live on large rural properties or they walk them in places where it's pretty safe to chase. Management is fine too. I'd also recommend a GPS tracker for peace of mind
I personally would not recommend a e-collar. You're going to be hard pressed to find any trainer certified by a reputable organization or behaviorist who uses them and for good reason. The vast majority of trainers who use them use pretty heavy handed, forceful approaches that compromise canine welfare. A lot of trainers will frame it as "you need to use this tool or your dog will get hit by a car and die" but management exists and dogs can still ignore e-collars. I've seen plenty of dogs who ignore their e-collars and rush up to my dog.
The reality is no tool, method or management will ever be 100% it's just important to mitigate the risk and to consider the training method from an ethical standpoint