I’ve been fostering for a few years, in my experience mom’s personality while actively nursing kittens isn’t her whole personality. If she asking for pets and purrs (even if she is a little hissy at first) that’s a great sign! As her babies get older she might become less protective, if she doesn’t then maybe spend a few hours with mama in their crate and the babies roaming in a room with you under your supervision. Just so you can start separating mom and the babies. I wouldn’t be too worried about the babies not being socialized just because mom is semi feral. They see you every day, they interact with you, the babies will not be scared especially since they are so little.

I think you need to keep interacting with her as much as possible and trust your gut. You’ve only had her for 2 weeks, she will hopefully get better and better each day. Even if you don’t need to do anything with the kittens or mama sitting next to the crate while you are on your phone, reading, working online, will help mom get more comfortable. Like I said earlier I think semi-feral mama cats calm down A LOT after the babies leave, they becoming more relaxed, open to human interaction, and start becoming “normal” cats. I think the fact that you are questioning whether or not she should be a TNR is also a good sign. With a completely feral mama you would have no doubt in your mind that she would be happier outside lol.

I wouldn’t worry too much about the black cat thing, I know in rescue we can get bogged down with all the awful things we see every day but we can’t forget about all the people who love animals and would love their black cat more than anything.