Premise: I personally love longbows, an elegant weapon from a more civilized era.
I suggest this book to anyone interested. It's recent and with new tests:
Mike Loades - The longbow
So do not take the following as dissing the longbow or bows in general but
It is not that it is impossible. It's just not the wisest thing to do.
You do not mention the kind of bow your culture use, and many of the replies have assumed the longbow. For good reason, but let's go orderly.
First of all don't assume two different bows with the same draw weight are going to produce the same energy on the arrow or the same damage to the target. There are a lot of other variables at play.
The longbow for instance is efficient due to its long draw (around 30" depending on the archer) and long limbs. Observe how at full draw the angle formed by the string and the tip of the limb is smaller than with much a shorter bow. The bigger that angle the higher the stacking. Stacking is 'fictional' draw weight. Imagine pulling a piece of wood with a 180° degree angle. How much energy will be transferred to the arrow? None.
Still the archer feels that stacking and strains his muscles for it.
That is why bows that HAD to be shorter (for instance because used on horseback) were heavily recurved. To lower stacking and allow storing higher energy in the system while drawing.
Other designs (e.g. recurve, reflex / deflex) are even more efficient than the longbow but they need longer construction times and were more expensive to produce. Longbows could be mass produced, with several bows obtained from a single stave.
When it comes to defending a fortified position crossbows are going to be more effective than bows. Higher energy in the shot, easier to move around in tight places and to exploit cover and most of all easier to train with and to shoot for an extensive period of time, for instance in a siege which is most likely to happen when a force is attacking a fortified position. In the middle ages sieges were far more common than open field battles.
Of course your clan may have not discovered crossbows for some reason if you don't like them, it's your world.
But since you add the tag medieval I take you want some historical comparison. In England aristocracy would not train with the heavy longbow (they may use lighter bows for hunting) and would dedicate themselves to their proper role in battle. Archers were commoners. And were duly encouraged to train.
And so 1363 marked the first of a series of ordinances and parliamentary statutes meant to compel Englishmen to spend their Sundays and holidays “not in pointless amusements such as football, bowls, tennis and dice, but in shooting at the butts.”
Archery in Tudor England
Do you really want your daughters of the aristocracy to mix with the rabble?
Extensive training with heavy bows leads to a number of cartilage problems. Not something the aristocracy would impose on their daughters I wager.
Also consider their opponents, what kind of armors do they wear? As plate armor became more common the effectiveness of the longbow declined. Also chain mail with textile additional protection proved effective.
In 2011, Mike Loades conducted an experiment in which short bodkin arrows were shot at a range of 10 yd (9.1 m) by bows of 140 lbf (620 N) - powerful bows at less than normal battlefield range. The target was covered in a riveted mail over a fabric armour of deerskin over 24 linen layers. While most arrows went through the mail layer, none fully penetrated the textile armour.
Brigandine armour instead proved vulnerable to bodkin arrows.
P.S. Your clan must be made up of huge people! 1.78 as average for women? What do they eat?