As a rescuer of a Great Pyrenees with behavioral issues that no doubt stem from his ruff past, I can say with true sincerity I feel your pain.
My wife and I rescue dogs, so we have had to rehabilitate dogs from various states and deal with issues that most owners would have just given up on their dogs. For this reason, we tried almost any training or management technique you can imagine so please understand this when reading the rest of this - I don't want people thinking it's a good idea to use advanced forms of behavior management like remote training collars as a "try this first". There have been some times that I have been able to use a remote training collar effectively, but it's a device that I find I use only for short while during handling a specific behavior then it's put away. To give some detail, I would say I've used ours maybe a couple of times in the 5 or so years we've owned it.
How to approach training in general
When you say training to some people they think about making your dogs do tricks, to other people they believe you mean house training... the reality is, to a dog there is basically no difference between the two. To be successful at training - particularly in difficult cases, you have to learn the dog and pay keen attention to trying to discover why the behavior is happening. As humans we like to project our feelings on to dogs, so when we see them look "guilty" we think they feel guilt for doing something bad for example. The reality is, often times the dog is actually just aware that you will be upset and that is why they are acting "guilty". Merely knowing that you will be upset does not mean the dog understands why you are upset, and it's very important that you understand almost every time a training failure comes down to a dog not understanding, or being medically unable to comply. If we approach training like solving a problem, it becomes much less personal and more productive. It's always best to start off with the simple proven techniques, then work our way up to more advanced techniques when the basics aren't working. We never want to go right to the "strongest" training technique, but sometimes the strongest technique is what's required and is best for the dog. We have to make sure that when we get there, we are doing it for the dog and we have a very specific reason for trying that technique and aren't "winging it".
Do remote training collars work on a Great Pyrenees?
In my experience, the answer is a resounding NO. I don't say this because I am against the use remote training collars, used correctly they can be a very effective tool. I say this because I've used remote training collars on different dogs, and the single one that it was least effective with was our Pyrenees.
Great Pyrenees are -particularly- stubborn. They were bred specifically for being independent minded and strong willed, and anyone who has one can testify to that. It's completely normal for a Great Pyrenees to be difficult to recall and a training collar offers no effective tool against their stubbornness. Here are some specific reasons why I really believe you shouldn't use a training collar on a Great Pyrenees
- They have long hair, so if you're using a "shock" type, even with the long probes it's very likely to not contact at all
- In my experience using negative re-enforcement causes Great Pyrenees in particular to shut down and stop listening to you at all, so don't be surprised if it makes the issue of not responding to a recall much worse.
- Great Pyrenees have an amazing resilience and tolerance for any type of pain - negative enforcement is not a good motivator for this breed at all
Each case is different, but this is how we were able to overcome it. First to learn how to train your Pyr in general, you need to learn what makes him tick - what brings him joy. In our case, he likes being with our other dogs and he likes direct 1 on 1 attention. He isn't very food motivated, and he's really not toy/play motivated either which makes him a real challenge. We also know he loves going outside, and doesn't like coming inside when called. Armed with this knowledge, this is the technique we used
- Put the other dogs away so the training session is as free of distractions as possible
- Take the dog outside for a short enough time that he would be most resistant to want to come in, in this case about 3-4 minutes. Sooner than that he hadn't gotten engaged enough that coming in was easier. After that and he may have "had his fill" and be ready to come back in.
- Call him, if he comes praise the heck out of him and give him direct 1 on 1 petting and attention - over the top, you want to feel embarrassed if you find out anyone is watching (maybe also give him a treat - in my case he often wont eat a treat).
- If he does not come back when he is called, keep calling him until he comes to you, then gently lead him by the collar into an area of isolation (in my case, we used the crate but you can use a bedroom or anything). In the case of my dog, this is because he gets his happiness from being around others and it's merely used to give him something to contrast with his reward for doing it right. It's important to understand we're not using the crate as a form of punishment - you should never associate a crate with punishment. I would leave him there for about two minutes and then continue. Keep in mind that if you have a problem with him acting out while in isolation that issue should be handled before this training can work - you don't want to take him out of isolation while he's acting out, as it will re-enforce that behavior and make it worse
- Let him continue playing for another time interval and repeat the process until he succeeds 3 times in a row, or he is no longer interested in playing. If he succeeds 3 times in a row, give him a "lottery" reward which is like a whole bunch of treats and 3x the praise and reward as before. If he stops being interested, that's fine just try again some other time but no lottery reward unless he gets it right 3 times in a row.
Is he ready?
If your dog isn't responding to any type of training at all, he may not be ready for it. This was the case with our Great Pyrenees for about the first 6 months after we rescued him. As is the case with many rescues, his past is completely unknown - he was found abandoned by his original owners. He also traded hands a few times before we got him, and when he first arrived at our home he was not the most pleasant dog to have around. It took us a while to learn his needs, and for him to learn that he can trust us. While this process was happening, there was very little if any productive training happening. If this is your situation, the only way to get through this is to provide tons of positive support and trust building and avoid negative encounters - even just firmly saying "no" was enough to make our Pyrenees totally shut down during this time. We had to just praise him when we 'caught' him doing the right things, and do our best to ignore him acting out. Now that it's behind us, we are able to treat him like any other dog and saying "no" doesn't make him shut down, but he's still just as stubborn as he's ever been!
Sorry for such a long reply. As I'm sure you can see, you managed to ask the very question that aligns with what was a huge barrier I had to overcome. Hopefully what I've learned from my experiences can help you and your Pyrenees out too!