Are Muslims allowed to have sexual relations with married slave women?

 Islam neither allows rape nor permits committing adultery [zina] even if it is done by mutual agreement.
- As for milk al-yameen (female salves), it has nothing to do with rape. Rather, marrying female slaves is allowed by Allah Almighty in the Shari'ah. He regulated and has set certain rulings for it. This is the same as He allowed marrying free women according to certain rulings. Both cases are revealed by Allah where there is none to put back His command. 

- It is only allowed in Islam to enslave [women and children] who reside in countries which are at war with Islam [Dar al-Harb or abode of war]. As for those who do not fight Islam, it is principally disallowed to enslave them. Capturing a person at war is easier than killing him. If enslavement occurred, Islam has set certain etiquettes for its followers to abide by towards treating the slaves. It urges Muslims to treat them kindly, not to harm them and prohibits aggression against them.

- The hadith mentioned was narrated at a time when none has called for abolishing enslavement. Moreover, taking prisoners is legally approved by all the countries of the world since non-Muslims used to capture Muslim women if Muslims were defeated. This prevailed until the international agreements issued the laws of putting captives to prison and the other practices that Muslims abide by now around the world.

- As for claiming that there is a hadith in which the Prophet (pbuh) permitted Muslims to rape the wives of the disbelievers before their husbands, it is absolutely erroneous