Is it permissible to allow one's brother and his wife into the home, knowing that the brother committed adultery with his wife before the marriage contract and that she bore him a child out of adultery before the marriage contract?

If the marriage contract with the girl's mother was concluded before the pregnancy became apparent, and the girl was born six months or more after the contract and consummation, then she is his daughter and is attributed to him.

The contract is considered valid, so there is no harm in allowing them to enter your house. You should advise them to repent and conceal their past.