I want to talk first about Catelyn Stark and Cersei Lannister. In the show (GOT) and even more so in the books, we see an interesting relational calculus. On one hand, they are thrust into marriage for political reasons, for the benefit of their families. (As are Ned and Robert, for that matter--remember, Ned is forced to the altar when the original groom, his brother, is murdered). On the other, we see that both of them gain power and authority of their own out of the deal--authority, defined by the position into which they are thrust; power, defined by what they make of that role.
This offers us a useful way to think about the subordinate yet complicated place of women in Latin medieval society, particularly with respect to their intrafamilial roles. Most of my answer is going to focus on the elite classes--nobility, urban gentry--because that's where our sources lie. However, one noteworthy aspect that emerges from manorial and parish (church) court records from late medieval England, at least, is the attempt of parents to control the marital destinies of their children down to the poorest peasants, even where no or little property seems to be at stake. Daughters, after all, exercised enormous economic importance within the family--caring for younger siblings, rural peasant girls fishing, urban gentry daughters helping run the family workshop.
The classic, even stereotypical example of daughters deployed for the benefit of their families/countries is the marriage alliance. On the surface, this would be a better deal for the groom's family and the bride herself. It represented an outflow of money from her natal (birth) family to the marital one. Children of the marriage would generally be accounted part of the marital family. In urban Italy especially, where newly married couples generally resided in the home of the groom's father for years and even decades, this could have tragic consequences. The custom was for a middle/upper-class widow to return to her own father's house, leaving behind her children. (North of the Alps, widows were sometimes able to carve out success as a head of household instead).
But marriage alliances were not just about the husband, wife, and future children. In the moment, they opened up a line for diplomacy. Especially when we think of the landed estates and counties of HRE/England/France, women traveled to their new homes with an entourage. They sent letters back to their natal relatives with messengers and ambassadors. These connections provided invaluable opportunities for negotiation and diplomacy as well as espionage on the part of the birth family.
Of course, much of the effectiveness of this role would depend on the woman herself. Kunigunde of Austria--princess of the Holy Roman Empire and eventual Duchess of Bavaria in the late 15th century--is a great example of how women worked to aid their families as both daughters and wives. The stereotypical role of the married medieval noblewoman is "mediatrix": interceding between petitioners and her lordly husband, ferrying their requests, pleading on their behalf. Adolescent Kunigunde was an active behind-the-scenes player in her father's court. Her biographer records numerous occasions where she played a pivotal role in either winning someone an audience with the emperor, or influencing her father's view on the subject.
As Bavarian duchess, however, she continued her allegiance to her natal family. When she thought her brother (then King of Romans but I think not yet emperor) and his wife had been fooled by a false holy woman, she endeavored to uncover the spiritual con artistry. At the same time, she was committed to her marital family, choosing to retire to a convent in Bavarian ducal patronage.
Placing daughters in designated convents was another family strategy--albeit one that could offer women one of the best chances to exercise personal ambition. The definitively medieval component of this geopolitical world was the growing entrenchment of the Church as an economic, political, social and cultural power. The Church collectively was the largest landowner of the Middle Ages, with individual abbots (even abbesses) and bishops acting as formal secular lords in addition to being spiritual leaders of their communities. The straight-up political advantages to placing a daughter or son in a prestigious house are readily apparent. We even know that lords manipulated the elections of abbots/abbesses and transferred children from one house to another for their political gain--even above the protests of the children or their current communities. Hildegard of Bingen, for example, fought bitterly to keep one of her closest friends residing at the Rupertsberg, but ultimately Richardis' family was too powerful for even the great 12C magistra.
To medieval people, placing a family member in a religious community--especially a prestigious one--also increased their spiritual power, that is, their bargaining position with respect to the ultimate heavenly authority. Forging ever-closer ties to a convent whose #1 job was praying for the souls of its patrons, they believed, would speed them to paradise after death and maybe even aid their fortunes in this life.
But connections with convents could likewise go both ways. First, the Church strove throughout the later Middle Ages to limit lay power. Monastic reform movements repeatedly sought to ban child oblation, the practice of nobles pledging their children to a particular community. They wanted people to come to monastic life only of their own free choice for their own spiritual benefit. Second, once in the Church, nuns, monks and non-ordered clerics often had a way of acting for their own benefit or Church benefit instead of their families. It's true that Hildegard was a master of controlling her public narrative and so could have smudged out any signs of acting on her family's behalf (to promote the view of herself as a prophet and saint)...but it's very difficult to see her actions aiding her natal family directly and purposefully. And of course, monastic life offered women the rare chance to exercise authority from office, not just behind the scenes.
Growing urbanization and the rise of humanism in the late Middle Ages gave rise to another way fathers, specifically, crafted their daughters to promote family and civic prestige. The Renaissance "learned lady" could become almost an intellectual patron saint of her city--until marriage, at which time she was expected to recuse herself from the republic of letters and ideas to be a proper cloistered wife. Fathers in Italy and Germany, especially, employed private tutors to teach a favored daughter the strands of humanism deemed acceptable for women--Latin, Greek, Scripture, but never the stuff of political engagement. Cassandra Fedele of Venice and Caritas Pirckheimer of Nuremberg gained international reputations as ladies of learning, helping forge a reputation for their cities as centers of culture and learning.
A poignant example of this trend is the fate of Juliana Peutinger, three year old daughter of relentlessly ambitious Augsburg humanist and civic official Konrad Peutinger. Determined to make his family and city shine for the visit of the Holy Roman Emperor, Konrad and tutors spent the better part of a year beating (possibly literally) into Juliana's head a memorized Latin oration to recite. Peutinger himself succeeded: the text of little Juliana's oration (ghostwritten likely by him) continued to be printed even two decades later, perpetuating his family and city's imperial grandeur.
For her part, Juliana demanded from the emperor "eyne hubsche Tocken"--a pretty doll.
Overall, we can definitely say that women played a crucial role in family, national, and civic strategy in the Middle Ages. But that role was really "roles": a complex negotiation between parents and daughters, husbands and wives, laity and Church; changing over time and geography and individual cases. Sometimes, sure, we can say that fathers "used" their daughters. But women had their own views, and could sometimes forge places and power for themselves by using and subverting the norms of a patriarchal society. They might do this for their own ends and/or the ends of their families--old and new.