Can you not put your dogs in kennels for those days, or hire a dog walker sitter there are plenty about as they are very much needed by many people today for instances just like this. There should always be an option for someone other than yourself to care for your dogs.
Although I fully understand being a dog owner how you feel. I think you also need to look at it from your employers side. Is it really your employers fault that you have dogs?
It has taken womens rights so long to get equality in the work place due to childcare issues where women were passed over due to emergency childcare being needed, days off etc, we surely do not wish for people with dogs to be judged the same do we? If you have a dog and work then it is up to us to find care for them not take days off work or miss training courses because of them, otherwise employers are going to treat dog owners as no go areas as they can not give 100% commitment to their jobs.
Your job pays for your food, bills etc so I certainly would not be upsetting my boss over my dogs care, IMO I would go on the training course as others are having to and arrange for a walker to come in for your dogs.