Your puppy should only be reasonably expected to hold it in his crate for about how many months he is old plus one, in hours but this only a very general estimation. All puppies are different. Also, do not start by calculating this based on our puppy's age and start with 4 hours. It should always be a gradual increase. Again, this varies.
I do not have all the information, as for how long he held it during the day in his crate for three days before he started peeing in there, but my guess is that it was either too long, or he wasn't emptied out before being crated. My instinct is that he did try to keep his immediate environment clean (his crate) for those three days but now he realizes he's not going to get out in time to relieve himself outside of it, so he has given up and is messing in there.
You will now need to back up and start over, gradually increasing the time spent in the crate but right now during waking hours, I would do no more than an hour. Explaining the entire process here is very time consuming so this article has some information:
Housesoiling | Dog Star Daily
As for the bath, when he is quiet, give him a treat each time and very quickly so you catch the quiet behavior. I know you have to get the bath done and remember that for every action there is a reaction.. so.. bark/whine = no treat and the second he stops to take a breath, pop a treat in his mouth. It may only be a millisecond at a time and timing is everything. This is just one way to do it and I'm sure others will give you more advice.