Ginevra Requests the Honor of your Presence and Critique

I'm just going to go with metric fixes here because I like the poem overall so there's no need to really critique any part of it -- it says good things goodly

I would like you to keep the rhythm you have in the first line.  For me it scans a little different to ole A of Y and I like it, it's kind of in-your-face.  So... 

You/ SAY your de/ SIRE burns a / LIra for / ME -- aside from that first syllable, which is unstressed and we can safely ignore it (many lines start this way and it's fine) this line is in dactyls, which are triple feet (DA dum dum -- 3 syllables per foot) rather than double like iambs.   This speeds the rhythm up and makes it more lively.  The last single accented syllable makes this what we call a truncated line, in that it doesn't include the last two (unstressed) syllables of the final foot.  That's not uncommon with triple feet like dactyls and anapests (which are reverse dactyls, da da DUM).  Homer used it so it's cool for you to do it

but/ COOL is the/ SHADE ‘neath this/ JUNiper/ TREE -- I've just stuck in an "is" to stretch out your meter properly.

You/ LEAD me from / HOME
Tend/ FIRES of your/ OWN -- very tiny fixes here, the change in the meter is nice and again, not uncommon with dactyls, it's almost limerick-ish.

But stroke and frame my alabaster beauty. -- this is flat out terrible for meter because to get it to work you'd have to stress that final syllable of "beauty" and I'm sure you agree that just isn't right.  I am not sure what to do here but in all honesty, nothing about this line works.  Plus, "alabaster beauty"  has been done to death.

a/ PITy you/ WON'T divine /DEPTHS that I / HIDE -- this is not an ideal fix either but just for meter's sake it works this way

pray these embers in my heart do subside -- another line that just doesn't work.  The inversion of syntax "do subside" is very awkward and it just yells that you've forced it in to fit the rhyme.  It is also not clear who's doing the praying, whether it's a plea to self or a directive to another.

My/ INtellect/ KEEN,
a / SONnet, a / DREAM
He / FANS flames of / PASsion at / Evening /TIDE -- only metric fixes here.  Symmetry is very important.

Power and wealth may seethe gold rings to impress -- are you sure you want "seethe" in there?  It's not logical for me and although I get the gist of the line I'm not sure precisely what you mean.  

but/ UNder these/ BANDS poli/ TICS sparks du/ RESS.
Take/ CARE you don't / BURN
for/ (SOMEthing I) YEARN; -- I don't know what to put in there but leaving it as is would not be great.

The / SOUL of a / WOMan may /NOT be po/ SSESSED

I do hope that helps a little.  Meter is NOT easy until you have that CLICK-aha! moment, and then it falls into place and you wonder how you ever struggled with it.  It will happen.