tell them the kitty is stray, and you're doing TNR (trap-neuter-

would offer a discount (feral cat package), sometimes even free fixing.  But you must bring the kitty in a human trap (the metal cage your Indian neighbor used).  If she lets you hold her, then you can place her in the trap, insteading of really trapping her.  Cats become extremely scared when they're trapped.  It can be a really traumatic experience.  Once you have her in  the trap, if she is restless, you can place a dark shround on the trap.  She'll then calm down.  It's hard. But it's good for the kitty in the long run.  Make sure the kittens are weaned before you get the mom fixed.