Monastic writers of the 11C famously divided Latin medieval society in three groups: those who work, those who pray, and those who fight. The ideal expressed by the third group was elite, landowning men (the concept of "nobility" is evolving rapidly in the 11-12C) owed periods of military service to their lord in exchange for holding land. Of course the legal reality of the situation was messy: a count might hold some land independently, some land from one prince, some land from another. By the later Middle Ages, too, monetary payment might well stand in for military service. The martial reality of the situation was messier still: prince-lords marauding across the countryside of Europe, kidnapping each other's merchants for ransom, torching fields, building castles (strongholds/claims to land) against the express wishes of their king, terrorizing peasants.

Women, although systematically excluded in one sense from "those who fight," played a crucial role in this system. When lords were away--whether at war or diplomacy--they would designate a regent to run their estates in their place. Traditionally, although not necessarily, this would be his wife. Christine de Pisan, writing in the late 14/early 15C, denounced the stupidity of a sexist system that expected women to know reading, writing, figures, and politics to govern, while explicitly denying them the chance to learn how.

Still, countless women rose to the occasion. While her ill-fated husband was off being a bad crusader, Adela of Blois garnered praise from Crusades-era chroniclers for her apt handling of the estate. These women would not typically take up arms themselves, although there were exceptions. Jeanne la Flamme or "Fiery Joanna" of Flanders traveled to one of her husband's cities with a siege looming in its future to head up the defenses! If a lord died while his designated heir was still a minor, there would be a regent appointed until the (typically) son reached the age of majority. Some women did fight for influence in that position--Adela maneuvered quite skillfully to maintain her power during her son's minority.

The era of the First Crusade, late 11C/early 12C, witnessed the birth of the ecclesiastical knighthood or military monastic orders, most famously the Knights Templar. We do know of some Hospitaller nuns. However, much like their Second Order mendicant sisters (Dominican and Franciscan/Poor Clare nuns), the Hospitaller nuns were excluded from the fighting responsibilities of the male order. Hospitaller women are said to have assumed some of the, well, hospital duties of the men, but this is in line with standard women's monastic practices.

By the time we get to the chivalric orders of the 14C and later, we are talking about something different, and much more ceremonial. There were "Ladies of Garter" for roughly the first century of the Order of the Garter's existence (ca1350s-1488). This was an honorary rank for women, through and through. (And for the most part, for men as well.) While the Order itself has its legendary origin story in recognized combat prowess, by the end of the Middle Ages into the early modern era it was taking on more governmental/recognition of the king's good graces roles, such as responsibilities in parliament.

There is an interesting 17th century source that describes an "Order of the Hatchet," an honorary rank bestowed on women of 12C Iberia who bravely defended their city from Muslim armies. While there is absolutely zero doubt that women did take up arms to defend towns during sieges--one of the ways we regularly see women in combat in the medieval ages--I am skeptical of the historical veracity. (I would love to be proven wrong!) First, the creation of a knightly order after the fact to recognize military prowess hews much more closely to the origin stories of the late medieval/early modern chivalric orders.

Second, the 17C author writing about Spain recognized them as "knights" based on particular linguistic usage that he paralleled with Latin examples. However, we know the Latin and French versions of the term did not apply to women warriors in the Middle Ages but rather to the wives of knights. Ashmole, our 17C friend citing Spanish authors, was part of an evident medieval/chivalry antiquarian revival at the end of the century that tried to apply similar claims retroactively to French noblewomen. I want the Order of the Hatchet to have existed, and I would love for /u/TheGreenReaper7 to come tell me my skepticism is mislaid.

Ever heard of Joanna of Flanders? She was the wife of John de Montfort, who tried to press his claim on the Duchy of Brittany. After he was captured by the French she took over fighting for his rights and eventually her sons. By all accounts she was a real piece of work. When she was stuck in Hennebot, which was being besieged by the French faction. She rallied the populace to resist and donned armour and sword herself and led a charge out of a side gate with 300 cavalry, destroying the enemy camp in the process. Despite truly terrible conditions in the town she refused to surrender and retreated to England, gathered reinforcements and came back. On her way across the channel her fleet was attacked by a combined French-Spanish expedition. She, of course, took part personally fighting with a polearm in the centre of the fray and eventually beating back the enemy.

I'm not sure if this exactly answers your question about Dame Knights but it does prove that in extreme circumstances it was ok for women to take up arms and take on the normally masculine role as a commander and warrior.