Help with new cat, seems terrified.

This may be kind of long so I apologize in advance
I recently adopted a maine coon mix kitten who is 6 months old. I knew she was "a little shy" when I went to pick her up and I know it would take time and patience for her to be comfortable in her new home. When I went to pick her up she was being kept in a large dog kennel, along with her brother, in an empty house. The short version of the story I was told is... The landlord of the lady I got the cat from found a pregnant cat and took her in, I don't know if she was left behind by a tenant or if she was a stray. I am assuming they were kept in the kennel in the empty house from day one. She found out about them and started trying to find them a home, she said she would go over there daily to socialize with them. I was told it took awhile before they warmed up to her but eventually they would allow her to hold/pet them but whenever they were not being actively held they would run back to the kennel and hide. Fast forward to me bringing her home, I brought her in a carrier and opened the door to it thinking she would eventually make her way out. I quickly realized that being in a house with 3 small, EXTREMELY loud kids was probably traumatizing her so I moved her to my bathroom put her litter box and food/water bowls in there with her and left the carrier door open thinking she would eventually make her way out since she was in a more quiet area of the house, well quieter than the rest LOL. She didn't so much as MOVE for 2 days. She didn't come out to eat, potty, drink water NOTHING. So I took the top of the carrier off and the next evening while we were at the grocery store she finally came out and ate about half a can of cat food and decided to hide beside the toilet instead of the carrier. Now there are other areas she could have hidden in/behind that would have been more secure I guess would be the word. She could have hid in the litter box (which she did when I tried putting her in it to show her what it was), behind the litter box or behind the toilet. Being beside it she was somewhat out in the open. I've also noticed when she walks.. she kind of skulks, she hunkers down and her belly is touching the ground like she's expecting something to get her. Now if I pet her she will allow it, she won't come to me for it but she will roll around so I can get her better and she will purr so I am hoping that's a good sign.
My questions are...
*With her possibly having been in a kennel all her life will she ever feel secure not being in one? When I took the top of the carrier I was scared it might do more harm than good but at the same time I don't want her to hide the rest of her life. Should I put the top back on it?
*Is there anything I can do to help her feel more secure? How long should I keep her secluded and away from everything? I try to keep the kids out of my bathroom as much as possible and they know that if they go in there they are to leave the kitty alone for right now, they can speak to her in a soft voice but that's it for now. Also I make sure I go in there every hour or so and talk to her in a soft (motherish) voice, I will pet her. I try not to pick her up too much, mainly because I don't enjoy being scratched and she doesn't seem to enjoy being picked up.
*Should I bring her into the rest of the house for a short period each day or should I wait a little while before doing that? I haven't done that yet because I'm a little fearful she will get behind something and I won't be able to get to her and she won't come out at all.
Any advice anyone can give me would be great. I have never had a cat act this way before. We have a 3 yr old male (he was about 6 months old when we got him) and he was a little shy when we brought him home but that only lasted for about 2 hours, now he owns the place. Again I am sorry this was so long but I wanted to make sure everyone had all the info about the situation.

Thanks for the advice. I will definitely try getting the kids to read to her. It will help with their reading skills and help the kitten, wonderful idea. I actually thought about putting a radio in there with her but I wasn't sure if it would help but now that it's been suggested I may try that as well.
I've only had her for 5 days. She seems to be eating a little bit but I still haven't notice her having gone to the bathroom, at least not in the litter box and I haven't found any presents on the floor.
Our male (well my oldest daughter's lol) his name is General. He is her cat through and through. He's awesome! He's never scratched any of the kids, not even while playing. Sleeps with her every night and waits at the door and meows when she gets home from school. Sometimes I think he's part dog, I have never known a cat to do that before.
I haven't named the newest addition yet. I wanted to see what her personality was like first. I am seriously considering naming her mouse since she's so timid. Plus I thought it would be a little ironic to name a cat mouse, especially if she grows out of her timidness but I doubt I will. it almost seems cruel to name her that, no matter how cute I think it may be.
The first pic is General and the second is my new baby.

I think she may be slowly coming around, at least with me. I went into the bathroom this morning to feed her and to use the restroom. When I walked over towards the toilet, where she was hiding, I spoke to her so she wouldn't freak out and she started meowing, it sounded like our other cat does when he wants attention so I let me hand fall beside the toilet and she slowly made her way to my hand and sniffed me. When I was finished I sat on the floor with her and since she hadn't moved away from me I figured I could try to pet her and she not only let me but she also started head butting me, flopping around in front of me and kind of rolling a bit. She even followed me over to her food bowl, walking fully upright, and ate in front of me. She would take turns coming over to me to head butt me and going to her bowl for a bite of food LOL. She has the softest fur I have ever felt on a cat, she reminds me of a rabbit.
Later in the day when I went into the bathroom she was back behind the toilet but she meowed again I tried coaxing her out but she didn't come so I left her alone. I do think she investigated the room though because there was cat fur on the counter and in the tub.
Oh one thing I wanted to ask was while I was petting her earlier and she was going nuts trying to get more lovings her tail was shaking, kind of like a male does when he sprays. It was the whole tail and it looked kind of like a rattle snake tail shake... does anyone know what this means, if anything?

No on both questions but she has an appt on Feb 10th to be spayed and I am assuming they will check her out before hand right?

I'm glad we're making progress. I really do hope she will realize she's safe and loved. I just want her to have as perfect a life as possible.