PP, your h is teaching your child to lie to you. This is despicable and and alters their perception of reality; gas lighting.
It is especially damaging when these mind games are perpetrated on such a young, vulnerable child.
See an atty about a sep agreement. I have seen too many good people "take their time" right into bankruptcy.
And, I've seen a few whose spouses came back glad that at least one of them kept a sane view and made practical, ethical decisions regarding marital funds and child well being.