Tenant wants to break lease

[Viral Mehta]

Hey guys, 

I have a rental in Dallas and our tenants want to break the lease and move out early. I have communicated to them that I could accomodate their request by listing the house back on the market (for rent) and they would be liable for rent till the time a new tenant moves in as well as the associated marketing costs. 
The tenant is now not sure on their move out date. They want to move out once we find a new tenant so they dont have to pay for days when the house is sitting empty. Also, they want to list the house and find a new tenant. I have a few questions

1) Is it normal to list the house without knowing when the tenants will actually move out. They have commited to moving asap, once we find the new tenant but what if they cant move due to some unforeseen circumstance

2) I am leaning towards listing my house likely using my broker as opposed to having the tenant do the listing and coordination. Would you guys suggest otherwise? 

Thank you for your help.