Feral kitties

I have a dilemma. Two weeks ago a stray cat delivered 6 kitties in my chicken coop. She's a wonderful mom, I feed her and she takes great care of them. The problem is she did the same last year, delivered 5 babies, took great care of them, and I didn't disturbed them (following Sac shelter and SPCA advice) for more than 8 weeks. By the time I started trying to approach the babies so I could get them fixed and vaccinated, they were feral and I was not able to do it. 2 of them disappeared and my fear is they were eaten by the coyote, another one was run over by a car, the 2 left are still feral at my property. So this year I didn't want the babies to be feral and I have been petting them when I visit the coop, but I guess mama didn't like that, and tried to hide them somewhere else. I found them, put them inside a trap, and was able to catch the mama. SPCA asked me to set an appointment for spaying, I logged in EXACTLY at 6pm last night to do it, and all the spots were taken. Also, I'm not sure if the mama can continue breastfeeding after the surgery. The other problem is I'll be out of town the entire week next week, and don't trust my husband or kids to take care of them without letting the mom go (she's really feral) My questions: Should I continue trying to set the appointment for spaying? If so, how? Can she really continue feeding them after the surgery as the SPCA last told me? Or Should I surrender the entire family to Bradshaw shelter (the closest to me)? I'm afraid because someone told me this is a kill shelter and I don't want them to die If I keep them, can anyone foster during next week? Someone tells me the 2 adult cats that are still in my property need to be neutered, can anyone help me trapping them? Picture of the setup that I made to keep them for now U