If grouchy insists they go and go NOW, I would get the kittens NOW and then try to trap the Mama. But I would talk to him and see if he would give it more time but if he refuses, I wouldn't leave them there for him to "dispose" of.. What are they hurting there anyway? Out on the back of the property in a old car, what harm are they doing. I would ask him that and also explain that you need to trap the Mama and that will take time. The Mama needs to be trapped and fixed to prevent more kittens so in the long run, it would be better for everyone.

http://www.feralcat.com/trapinst.html