Holy control issues batman! Is your H in therapy? I sure hope so. He needs to realize that his freaking out about the your son getting a little bruise is more damaging then the bruise itself. Anyone who has been around little kids knows that they fall and get hurt a lot. Its how they develop coordination and learn about the world. As long as you a making sure that they aren't going to get seriously injured I don't really see a problem. Often times when they do tubble they will look at the adults around them to gauge their reation. If the adults start freaking out it can send the little one into a panic as well. Calm adults make for calmer more confident children.
You say that things got worse after the birth of your son? I wonder if your H is terrified of failing as a father. If maybe he wants to protect his son from everything bad in the world because he didn't feel protected? He may get angry with you because you don't share his sense of panic? Maybe he isn't in a rational place where he realizes that falling down is improtant because it is how we learn to get back up. This is a hard one because if my H had been violent with me I wouldn't allow him around our kids for two reasons. 1) because he could become violent with the kids 2) because even if he is only violent with me that behavior is so damaging for both me and the kids.
It sounds like you have already tried to compromise by asking him how the house could be safer. And also if he is so concerned about them getting hurt why wasn't he the one watching your son like a hawk and hoovering over him as he tried to climb into his chair? I would set some frim boundries in place about his behavior. I would have him and myself both get therapists and work toward creating an emotionally and physically safe parenting plan for our son. I would want to talk to his therapist and get their opinion about the likelyhood of him being violent or volitile with our son. And all of this is based on the assumption that you are a good mom who isn't endangering your kids but perhaps just has a different parenting style than your H.
That's my two cents about it.
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Everything comes from within