Unfortunately, faults are very good at hiding from beginner writers. However, if you want to be published you have to fix them.
If you can't work out where to start, put your story away for a few weeks, preferably at least a month. You need to be able to read it with a fresh mind, as though it's new to you - or at least as new as is possible to its writer.
When you get back to it again, ask yourself a few questions. Does it still give you that rosy glow you felt when you finished writing it - or do you now feel a vague sense of dissatisfaction? If the latter is the case (and it almost certainly should be) but you still can't work out exactly what's wrong, you can always start with little things. What appear to you as small faults will look like huge ones to an editor, who will instantly be dragged out of your story by them. If you can't keep her focused on the story (editors of children's books are nearly always women, so I'll stick with feminine pronouns) she will definitely reject it.
Books (and even short stories) for children are becoming shorter as the years pass, which means today's children's writers must use fewer words than in previous generations. Therefore, every word must count. So, assuming you didn't find (or have fixed) any problems with the actual story - wrong time lapses, sudden changes in a character's eye colour, contradictions and inconsistencies (such as having a character's hands tied up in one scene and in the next having the character wave them around without someone having first untied them), etc. - you can now get rid of redundancies. Here are a few things to look for:
a bit, a little, about, actually, almost, almost like, already, appears, approximately, basically, close to, even, eventually, exactly, fairly, finally, here, highly, just, just then, kind of, mostly, nearly, now, practically, pretty, quite, rather, really, seemed, seems, simply, slightly, so, somehow, somewhat, somewhat like, sort of, suddenly, then, there, truly, utterly, very.
Your sentence will usually be improved if you delete any of the above words. Try it. You can always go back to the original sentence if you feel it really needs the word. (Sometimes it does!) Other phrases to look for are "begin to" and "start to." In most cases, for instance, it's better to simply have your character run instead of start to run.
In "She cuddled the tiny little kitten close,quot; little is redundant. This type of redundancy—two words together that mean the same thing—is used for emphasis, in this case the size of the kitten. When you find yourself reaching for two synonymous words, try using the strongest one on its own. It’s just as effective!
Many adverbs are redundant, especially when they’re used to tell how something was spoken.
In all of the following sentences the adverbs are redundant because it’s obvious how the words were spoken.
Other Often Redundant Words:
Are "that" and "had." Try deleting them. If the sentence doesn’t make sense you can always revert to the original. Especially avoid using "had had." It’s very ugly. Rewrite your sentence to avoid it.
In "She nodded her head," the words "her head" are redundant: you can’t nod anything else but your head. In "I thought to myself," the words "to myself" are likewise redundant: you can’t think to anyone else but yourself. "To her feet" is redundant in "She rose to her feet;" you can hardly rise to your hands or your head.
Would and could are often unnecessary, too. For instance, rather than "She would have expected to find nobody home," try "She expected to find nobody home." Instead of "He could sense that nobody believed him," try "He sensed nobody believed him." If the sentence works better with the "would" or "could" you can always put it back.
Look for every use of the word "was," which often indicates use of the passive ("she was told not to be late") instead of active voice ("he told her not to be late"). Try the same exercise with "were." Active isn’t always the best voice, of course. If you feel it works better with the passive voice, by all means leave it.
Go through your manuscript yet again looking for words ending in ly. See if you can delete them. If you feel the sentence needs the adverb, by all means leave it. If adjectives and adverbs were as redundant as some dopey self-styled writing experts would have us believe, they wouldn’t exist at all.