Mother cat isolated outside, HELP!

My cat had a litter of four kittens, 6 weeks ago. The kittens have all been eating solid food and every now and then mother cat will still nurse them. 

I heard that the mother will sometimes go out and bring back prey they have caught for their babies to feed on. Welp, this morning - to my surprise - my cat jumped in through our bedroom window with a live bird flapping it's wings in her mouth! I screamed and picked her up and immediately put her back outside with the bird still in her mouth. (Now, I had just woken up and my husband leaves the window open when it's hot out but we have a screen on the window. Except it looks like mother cat has created a hole in the screen so she can get out!)

From what I could see, the head of the bird was in her mouth and I did see some blood. She has now hid the body of the bird and is scratching at the window and meowing. She looks frantic and I know she wants to be with her kittens but I am afraid to let her back in! If she is still nursing the kittens, I do not want them to be tainted! 

What I am asking is, what do I do? Anyone else experience this?? 

What taint? That they'll become hunters also? It is innate. Cats hunt, that's why they chase Da Bird, scrumpled up paper, a laser pointer. If you think mama cat is tainted from the bird let me assure you that this is not the first creature she has caught and quite possibly eaten in the weeks between birthing the kittens and now.

Let her back in with her babies. She's still teaching them proper behavior. They love her, and she loves them - so clear from what you say about how frantic she is.

My biggest concern would be that if she is A) not spayed and B) allowed outside on a regular basis that she's already pregnant again.

Agree, let her in as soon as you can.  I too dont really understand the problem nor the question. You dont want her to teach them to hunt? So make sure she doesnt go out again.   But they all can the basic of hunts, even purebred inside only cats since many generations can do some hunting,  as you see in their merry play.

I agree also with Catapault spay her as soon reasonably possible, dont wait.   Make also a new deworming.

Good luck!