The stray cat had kittens in my wood pile! Update w/pic pg 1

So I had been feeding what appeared to be a stray cat who I noticed was pregnant.  She is really a baby herself.  I had placed a rubber made tote with a door cut out of the long side with old towels on the porch by her food in preparation, but while she had been in it, she had them in our wood pile instead.  She didn't look very big and I was surprised that she had them so soon.  She is skittish, but friendly.  Before she had them, she would sit and eat by us, but wouldn't let us touch her. 

We would never had noticed where she had them, but we wanted a fire randomly on Monday night and my daughter found them.  She had two adorable babies.  One mostly white baby with large black splotches, and one mostly black baby with white paws and belly.  We check on her a few times a day and have moved her food bowl back by the wood pile, along with the tote in case she wants it.  In a couple of weeks, I imagine that she will want to contain them a bit more.

She will let us look in on her, but I wouldn't dare try to touch them.  I'm sure she would take our hands off!  I also don't want her to cart them off somewhere or abandon them.  She obviously feels safe at our house since she had them here, but I want to keep the babies so I need to start thinking about ways to handle them so they aren't feral, or kinda feral like her.  And I want to get her fixed too (and the babies of course when they are old enough).  My DH is against this, as he thinks that she belongs to someone else, but I am just pissed that people get a cat and then don't get them fixed.  I'm also of the mindset that inside kitties are safer/live longer.  

I've had cats my whole life, but I've never had a momma cat with kittens before, let alone a semi-feral one.  How do I make sure that the kittens don't end up semi-feral while also ensuring that she doesn't abandon them or take them somewhere else? 

I already have my own indoor cats inside, so bringing her inside (if I could even get her to) seems like it would be more stressful for her.  I don't have a garage either.

****Update****

I seem to have worried for nothing.  Momma cat was eating on my porch this afternoon and was howling at us.  I opened the screen door and she cautiously slunk right in.  She had a bit of initial freaking out when she couldn't get back out.  I went and got the baby and the Rubbermaid tote bed that I had made her and set her up in the bathroom.   I didn't put the lid on it this time and that seems to have been why she didn't want to be in it originally.  Surprisingly she has not howled very much at all.  We have been periodically checking on her and momma and baby are perfect!  She is curled up with the baby in the tote purring away and has even let us gently pet her, although we are letting her run the show as we don't want to push it with her.  I am so relieved that they will be safe and that she doesn't appear to be stressed immensely by being inside. 

I have a picture on my phone of the baby that I will try and post.

Melissa