As the last post said, if your daughter & baby want somewhere to live they must NOT stop paying off the rent arrears. If they do, they will be evicted & the Council will not have any duty to rehouse them. It is even possible the baby would be taken into care.
So long as the joint tenancy remains, the ex b/f could return to the property and your daughter could not legally prevent him living there again unless she gets a Court order. If he won't agree to have his name removed from the tenancy agreement the only way of dealing with it is:-
1. Your daughter approaches the landlord, tells them the situation and asks them to confirm in writing that - if she gives notice to quit under the present tenancy agreement - they will then give her a new tenancy in her sole name.
2. Once she has the written agreement, she gives notice to quit. This is binding on the ex as well as on her.
3. The landlord then gives her a new tenancy.
IMPORTANT Be very careful about doing this - you have to get the landlord's agreement in writing, it must be unqualified and you must be able to trust the landlord to carry it out.