This is what I see as the Orders strengths and weaknesses...what do ya think?
Strengths of the Order:
Bards, Bards, Bards: Anytime a bunch of bards can work together they seem to enhance each others abilities. When you have an entire Order of Bards it just begins to get scary. If one fails to charm, there are always more around. Bards also know way to much and having an entire order of them allows different bards to become very knowledgeable in one or two fields which then aids the others.
Center of Power: Nearly everyday and for many hours a day the Order is in the palace and attending various members of the Royal Family. This gives them near unparalleled access and some claim far too much influence. Being the unofficial protectors of the Royal Family often lets them layer the children from those that want to gain access to them.
Wealth: For their size the Order has a lot of gold. Stipends from the crown as well as very favorable tax rates and their own ways of making money has made the order wealthy and has enriched many a 'Lady' over the years.
Secrets: Over the years the Order has found out many secrets and uncovered many plots. This makes them dangerous to those that would try and use the crown for their own desires.
Weaknesses of the Order:
Bards, Bards, Bards: When even the lowest Lady is forced to become a bard it skews the abilities of the order. Like House Branas completely martial leanings the Order is often to focused on bardic ability and performing when they should be expanding their skill set.
No True Loyalty: Though the order is very influential they have no real allies save the Grand Prince and the Royal Family. There are plenty of houses that if attacked could call on aid from other sources. The Order has to rely on the Grand Prince or their own abilities.
At the Center of power: Being Bards they all have the ability at some point to make suggestions, not the normal kind but those bardic kinds that can make a normal man crow like a duck. Add in they are always around and who knows maybe they are the ones that have caused all the problems for the past 500 years.
No Martial Present: Save for a small house guard the order has no military and really cannot hire a mercenary unit without many questions being asked. So an all out military move on the House would force them to abandon much of what they have built and try and convince the Grand Prince to send out the army in their support.
Nonhuman and all female: Does anything else really need to be said?
Okay.. notes. I wasn't actually picturing them as completely nonhuman, it's fine, but simply on law of averages it would have seemed like they have some human membership. Taldor having mostly humans in it, the Order would basically have to actively seek about to fill its membership with nonhumans. Something particularly more exotic like a catperson, you'd need to hit the slave markets of Katapesh to find, buy and train and free one, for instance, so, not impossible, but something to adjust for conceptually.
Similarly as far as weaknesses, unless you're trying to join the aristocracy, being nonhuman is not really a weakness in Taldor. Being a woman is in various ways, sure.
If you want a measure of social disdain, and it seems as you do, and from the way you've been describing your order, I'd want something like;
"Enmity of the anti Qadiran faction: The Grand Prince having at his disposal what can look to some like a stable of exotic, expensive prostitutes he himself does not pay for the services or companionship of looks to some to resemble the harems of Qaidran Princes and Princesses. This is not a flattering or well received comparison, and being relatively young to Taldor, several more ancient bodies remain displeased by the Order's existence, all of them aligning neatly (and somewhat ironically, given the origins of the order) to those advocating most strongly for war with Qadira. The Licinianus family tends to be at the forefront of such expressed displeasure, along with those they hold influence over. Andronicus Branas has made no particular comment one way or another, but a cold, thousand yard stare of grey eyes, harsh and desolate as the deserts he wages war within, are a difficult thing to read for any impression on any topic generally. Regardless of its source, that antipathy can be a stumbling block to Order efforts to expand their influence or reach out to any particular figure."
Also, off some other things I noted, there should be something in weaknesses to reflect that the order's influence tends to wax and wane with how comfortable any particular Grand Prince is with directly engaging their services. Any that are more reserved aren't likely to be (Stavian III, as you can tell from his picture, is not one of them, sure), leaving the Order with a few generations where they have had to rely on their services being availed on by the aristocracy generally to get by as far as finances. Imperial recognition only goes so far when a Grand Prince is otherwise keeping them at arm’s length. Include that in the no true loyalty bit.
Similarly, the center of power weakness. If it comes off like your Order are magically influencing the rulers of the nation, there would be a rebellion.