I've been in a slightly similar situation from the dog owner's point of view.
We had a collie called Roy who was placid, not had much to do with small children as my 2 lads were teenagers, but trustworthy enough.
My stepson and wife and 2 year old daughter called round and Roy went of his own accord to sit in his bed out of the way. The child, Amy, was totally undisciplined at that age and left to rampage round the room. I was in the kitchen making coffee. Next thing there's a commotion from the living room. Roy had bitten Amy. Turns out Amy had been allowed to virtually dance all over Roy while he had taken refuge in his bed. The mother, although a dog owner, had seen nothing wrong with this and let the child carry on. My husband, while sat next to Roy's bed, had also seen nothing wrong with the situation, until of course the manure hit the fan.
In my book my dog had done nothing wrong and had actually gone to sit out of the way. In the incident with Roy I blame the mother entirely who should never have let the child trample on the dog. In your case you weren't there and I would blame he FIL who should have more empathy with his dog, which is not an automaton, and as the adult in the situation should have taken responsibility for your little boy's actions and explained to him how to play with a dog.
When my own children were little I made sure they respected our dog and his personal space.
In your case you weren't there. But in this situation - the child understands English. The dog doesn't and a 4 year old is old enough to understand boundaries.
In your situation I would let the dog come visiting with your in laws, but it's your house and looks like you need to make some ground rules! Possibly insist that the dog and child are in different rooms, or the dog caged or some arrangement that works for you, unless you are there to supervise.
I don't think you are being unduly sensitive at all. However you have to accept people as they are. FIL isn't going to change his attitude and neither is he going to take the dog to training classes. So I would put the blame on yourself (so to speak) and explain that you are overly anxious about your little boy and would hate for him to ruin the lovely nature of their delightful dog (
). So until your son is old enough to play unsupervised with the dog then they
must keep the 2 apart unless you are there. Don't argue about it. It is non negotiable!