She makes a difference

Well, first, I disagree with Stephan. Nothing's wrong with the meter on THAT line.
Just say L2 like you were conversing casually with a friend. Would you really say to her, "That HAS been SO gent-LY pol-ISHED by YOU"? Just say the same words naturally, and see where the stresses naturally fall. You can also check a dictionary for the stresses (stress'-es).
Sometimes this natural-speech thing doesn't work - I always speak "chi-eld" when it's actually one syllable, but it's a good starting point. Some words, like "stalwartly" simply cannot be made iambic. (It's STAL-wart-ly). Still, even Shakespeare cheated a bit here and there. Hope this helps.
Alcuin
PS: I admire your grit - you're almost as stubborn as me, you poor thing.

Sorry Shannon, I know I said I'd get back to this and I am quite prepared to take my punishment for tardiness...

Point one:  Never take Stephan's advice on meter. 

Point two:  I'm sorry to disagree with A of Y, but stalwartly is fine -- some words are more strongly iambic than others but since you follow it with a soft syllable (comMIT) then it does work.  Once you're in the rhythm pretty much any words can fit, as long as you're not completely switching around their natural stresses.

L2 is a problem though.  For starters, it's not iambic unless you really force it, and if you do that it sounds dreadful.  You'd be better of changing your end rhyme there and going with something like "that's been so gently polished by your hand".  You'd obviously have to change L4 then, maybe "to give the children ways to understand", which does away with the "child" issue (I find my pronunciation alters depending on the words that are around it, much like "fire").   

L6 is, strictly speaking, iambic -- but it does force it a bit and I'd suggest a change.  Perhaps "with vivid strokes she paints tomorrow's world".

This brings me to another problem.  World is almost always rhymed with unfurled.  You really don't have a lot of options with words like that, but it actually makes the rhyme almost a cliche.  I would actually suggest changing the end rhymes there, because really, unfurled is hardly ever used except to rhyme with world!

You have inverted the syntax in L8 and again, it's letting the form dictate what you write.  Inverted syntax is not a problem in itself -- many people use it to great effect -- but it has to be words that really add to the piece. It's best to avoid it if possible -- "greatness swift" is bordering on an archaism anyway.

In L12, difference becomes a little bit of a problem, because really most people do say it as two syllables.  That's your call, of course -- it sounds very odd to me in this particular line, though you can get away with it.

In L13, you have a strong stress on MY, which is kind of unnatural.  Your daughter's name is Megan?  How about, "Without you shaping Megan's youthful mind"?

I think that's all for now...