Hi,
A court is most likely to award the council tenancy to the primary carer of the child - the parent with whom the child will live. If you are the main carer of the child it would be most unwise IMO to agree to a joint residence order ( previously a joint custody order). If both parents have residence as they do in joint residence orders, both parents have an equal need to provide a home for the child. The court's main concern is to provide a home for the child of the family and is therefore, most likely to award the tenancy to the primary/main carer, usually the mother.
It would be most unwise IMO for you to move out. If you are both in the house, the court will have to order one of you to leave, and will award the tenancy to the parent who is to remain in the home. If you have re housed yourself elsewhere, it is less attractive to a court to order the H out and make him homeless. If you are suffering domestic violence, the get him out immediately.
It is worth remembering that a council tenancy is a valuable asset. It houses you, and it confers on you a Right to Buy discount. Very rarely courts may require the spouse who remains in the house to compensate the spouse who loses the tenancy. Usually they don't. Only if your H were to be awarded the tenancy, should you mention compensation for the loss of this right.
If your H works, he can rehouse himself. Stay put, keep repeating that you need the house for you and your child, and that you cannot afford to rehouse elsewhere.
Change is considered bad for children. If you move your child will lose friends, may have to change schools etc. Remind everyone that having his parents divorce is enough change for your child, and that to lose his home would add to that detriment.
Good Luck