Would you consider my site a children friendly site?

It's definitely not a children's site.

It's not exactly "fun". I would use this as an example:

Top 15 Most Popular Kids Websites

Take note of some of the design work, and how tacky and fun they are.

Checked the site out and just by looking at it, I wouldn't have thought that it was a site built for children. To answer your question, the site is not really child-friendly but more on mom-friendly. I checked out the story section and it's mostly text, not too many pictures and the colors are plain.
-Try incorporating fun pictures (and maybe even sounds or animations) to it.
-Try putting in simple games for toddlers to do
-Try developing the color of the whole site (make it more fun looking)

My child wouldn't be interested if I read him a bedtime story from the site.

I have no idea of what you want me to do when i visit your site. Are you trying to get parents to buy from you?

I have 2 toddlers and what you have on your site looks like articles, not stories that I would read to my children. If you have looked at a kindle, iPad and even iPhone - what they have on there for stories is amazing! My son loves that he can touch the animals in the story and it makes sounds and at bedtime, he loves actual books. Then you have leapfrog that makes it so they can use their products to read themselves. If I were you, I would change up the whole site and just do children book reviews maybe? If you want kids to like you site, then put up a bunch of videos of you reading the book to a child. My son might find that entertaining, depending on how animated you were. Or dress up in a crazy looking character and read the books. You have too keep a child's attention.

One other thing to mention, the way you have the adsense in the middle of the story is not good. There is a way you can wrap the text around an adsense box. Now I'm also a newbie so sorry if I'm not explaining it perfectly but I just think the ads should be present, but not distracting to the point that you don't want to keep reading the story.

One thing to think about overall, your domain has "bed stories" and right away I think of bedtime. I only let my kids look at things like the iPhone or iPod during the day. At bedtime, I don't want TV or anything overstimulating to get them wide awake again. A nice book in dim lighting is perfect. Do you think parents want to have their bright phones reading these books or even a laptop in bed reading to them? Sorry, not trying to be negative but just honest. I just thought of another thing you could do with the site of children bed stories - do children bed reviews? Make up a funny story about each bed but still do a real review. Some of those beds can be pricey and parents do pay for it! Works with your domain and it could be creative ...just sayin

I tend to agree with OutsourceFactor .. it's more like mom-friendly rather than children-friendly .. lack of pictures and way of written stories ...

Thanks for all the solid advice, I appreciate all of it, and to the couple of people who didn't know what I wanted them to do when they visit the site, as you probably noticed there is nothing for sale on the site, so all I am trying to do is build up an audience. Thanks to all again.