"It seems I can not trust you even in basic things like putting the children's safety first. Disappointing and upsetting.
It still feels very nasty of you to say and do what you did. I am not sure I trust you with the children. It was not nice of you at all, cruel and awful."
Hearing this kind of stuff stings, and a silent treatment afterwards is just salting the wound. He probably
felt this way, and maybe still does. It's important for you to remember that these are
just his feelings and not some "objective truth" that you need to own.
The starting point is that you are both entitled to your own opinions about dogs. There is no right or wrong on this subject matter - and your opinions weren't even all that different. Children should probably not pet strange dogs, but that isn't what you were advocating. Nor should he impose his phobias onto the children - that's not fair to them (or the dogs).
As I see it, he is trying to impose his opinions on you and the children, which is pretty common for pwBPD. They are uncomfortable with diverging opinions and thoughts.
I hope you participated in your son't birthday present opening - he has no right to exclude you from this, and you need to enforce these boundaries. The children are not pawns in your relationship, but he seems comfortable using them that way. That is probably another area you will need to raise with at some point.
Don't chase him during the silent tratement. No more apologizing. Go about your business in a normal way, and let him come to you. He will.