Partial answer
The princess
is saying "Papa has drunk poison! Such rapacity, Hubert desires fathers throne, and my hand". (Simple-substitution cipher. I confess I just fed it to quipqiup.)
The embroidered cloth
has around its edges letter-indices saying "WEEP AS THE KING HAS BEEN POISONED WITH MURADITE AND LEDEBHTAEDSIHNOTF". That last bit (corresponding to the left edge) is a bit disappointing, but I can't help noticing that the last six letters are an anagram of FOHTIN. (Those letters also contain an anagram of ANTIDOTE but what remains after removing that doesn't look promising.)
Aha, MOehm in comments points out that
if when we reach the left edge we switch to reading top-to-bottom, we get ... LEFT ON HIS DEATHBED. So the anagram of FOHTIN may be coincidence, but in the absence of anything else to indicate the antidote I'm going to guess that the break in the reading order may have been deliberate, to put that anagram in a prominent place.
And
I don't know at present what to make of the numbers in the inner portion of the cloth; perhaps they provide either the key to the princess's cipher or information about unscrambling the left edge of the cloth. Reading in the "obvious" order and translating numbers to the letters in the usual fashion we get SBAIITLGRLHAYAP which is not obviously useful, and some of the numbers are too large to be indices into LEDEBHTAEDSIHNOTF.
Here again MOehm is cleverer than I am and points out in comments that
if you read those letters in the right order you get A BIG SILLY TRAP HA, which presumably means we should ignore them.
It seems clear that
there's no useful information in the geometrical patterns on the cloth.
So I reckon
the king was probably poisoned by Hubert using muradite, and I'd treat him (cautiously) with fohtin.
Incidentally,
I have some difficulties with the narrative here. I mean, princesses are capable of lying (and it's not so hard to imagine why someone who might be heir to the throne might kill the king), and someone seems to have done that embroidery ridiculously quickly, and in any case embroidering "the king has been poisoned with muradite" doesn't in any way prove that he actually was, and if you actually want someone cured then there just might be better ways to indicate how he was poisoned than embroidering the information in coded form onto a cloth. Frankly, in this situation I would suspect that actually Opal and the princess conspired to poison the king, that the cloth was done in advance as misdirection, and that the actual poison was anything else rather than muradite :-).