Returning security deposit to tenants who has bad breakup

[AJ M.]

My tenants were engaged at the time of renting the house 8 months go. Now they have a bad break up are hostile with each other. Each claiming the security deposit is their money. 

I have leased the house through a Real estate agent and as per agreement I need to return it to both of them. How can I do it? Write a check on both their names? or Give separate checks for half the amount to each of them? 

Also I would like to know my rights as a landlord in Dallas, TX...

The initial contract is for 2 years (I shouldn't have done it!!) and the guy is the bread winner and always paid rent on time. The gal has bad credit and poor income. We rented anyway, based on realtors recommendation, based on the guy's history alone.

Now the gal is saying he is a security threat to her 2 kids and keeping him out of the home. He does not want to pay rent any more so we can get her out of home. Even we do not want her in my home because of her credit. What are my rights to get her out of home?