It was common in most past ages of European society for parents or guardians to arrange marriages without consulting the bride or groom. And if the parents or guardians asked the bride or groom they were not bound by his or her desires. the parents or legal guardians could go ahead with the marriage even if their child was strongly opposed to it.
Though an official religious marriage ceremony performed by a priest as was usual for nobility and royalty would usually have a point where the two parties said they consented to the marriage. Thus the parents or guardians sometimes had to put a lot of pressure of various types on the engaged person to make sure he or she would give consent at that moment of the wedding.
But if one of the parties to the wedding was a legal minor then the parents or guardians had authority to give consent for the legal minor.
Being that her Mother is still alive at this time, it would only be logical that she is the only one who could decide who her daughter was to marry.
No. The father had superior authority over the other members of the family. The mother would only have the right to decide if the father was dead. And unless the parents of a person were the monarchs other persons might have the right or power to override the parental authority with superior feudal or other authority.
I do remember that Emperor Manual I Komnenos (reigned 1143-1180) arranged most of the marriages between members of the extensive Komnenos dynasty and members of Byzantine noble families and foreign royalty and nobility, for example.
Being that she is captive, being made to get married under duress would not make the marriage official , which would mean Tyrion Lannister would have no claim to the North
Monks were supposed to voluntarily take their vows of obedience and poverty, etc. But it was very common for parents to send minor children to monasteries until monastic orders began to prohibit it later in the middle ages. The biographies of many saints tell how they entered monasteries as young children.
Saint Bede the Venerable (672/73-735), for example, was sent to the monastery at Monkwearmouth, Northumbria, at age seven to be educated, and possibly with the plan to become a monk when older.
For example Liudolf (930?-957) was made Duke of Saxony by his Father Otto the Great (912-973) in 950. His daughter Mathilde was born in late 949 and became Abbess of Essen in about 965, and thus probably before her sixteen birthday.
Otto the Great made his daughter Mathilde (early 955-999), half sister of Liudolf, Abbess of Quedlinburg in 966, aged 11.
Becoming a nun was considered being married to God. If adults could "marry" off girls too young to make informed consent to God they could marry off girls to mortal men without the informed consent of the girls. So the forced marriage of a prisoner would not be too much beyond that.
Furthermore, captured rebels and deposed royalty were often forced to become monks and enter monasteries. Thus people could be forced to take sacred vows, so forcing people to take sacred vows of marriage isn't that much worse.
That they are married before the Gods, if is was forced, would the church accept it as official.
That depended a lot on whether the forced person made their objections publicly known - despite the possible dire threats of those forcing the marriage - and on how idealistic or cynical the local religious hierarchy was.
She is still a child even though she has "Flowered" (Tryion says this when protesting the arrangement to his father), I would imagine being the same as an under-aged person in current times
In medieval times minors could be married by the authority of their parents. And the church did have minimum ages for being married.
In 1176 a man named Sverre came to Norway from the Faroes Islands and took part in the long Norwegian civil wars, claiming to be an illegitimate son of king Sigurd Munn. After six years of war, Sverre became king of Norway. Sverre became a priest in 1175, and the minimum age for becoming a priest was 30, thus making him born by 1145. Wikipedia says that Sigurd was born in 1133, only 12 years before the latest Sverre should have have been born.
But the Medieval Lands site doesn't give a birth year for King Sigurd. It does say the sources imply King Sigurd was born before his father became king in 1130.
Thus King Sigurd could have been over 15 when Sverre was born. Furthermore, Sigurd's illegitimate son King Haakon II the Broad-shouldered (1147-1162) was born as early as 1147, just 2 years after 1145.
As Wikipedi says about the claim that as a priest Sverre was too old to be the son of King Sigurd Mund:
This particular objection has lost credence as it has become clear that this age limit was routinely ignored in Scandinavia at the time.
Thus it seems impossible to prove or disprove Sverre's claim to be the son of King Sigurd Munn.
And if Scandinavian churchmen often ignored the canonical lower age limit for becoming a priest, it is probable that medieval churchmen often ignored the lower age limit for marriage.
Princess Agnes of France (1171/72-1220 or after 1240), daughter of king Louis VII, was sent to Constantinople in 1179 and married or betrothed to Emperor Alexios II (1169-1183) on 2 March 1180. William of Tyre, who was present, described it as a full wedding despite Agnes being a few years below the usual minimum age.
Andronikos I Komnenos (c. 1118-1185) made himself co-emperor in 1183, and then had Alexios II deposed and murdered. Andronikos married Agnes in 1184 when she was 11 years old and Andronikos was about 53 years older.
In 1298, after defeat, Emperor Andronikos II Palaiologos promised to marry a relative to King Stefan Uros II Militun of Serbia (1254?-1321). He intended to make his widowed sister Eudocia marry the king, but she refused. Desperate to provide a bride, Andronikos selected his daughter Simonis or Simonida (c. 1294-after 1336) despite the shocked opposition of the Patriarch of Constantinople and many family members.
They were married in Thessalonika in spring, 1299 when Simonis was five and Militun was about nine times as old.
On 15 January 1478 Richard Plantagenet, Duke of York (17 August 1473-1483?) was married to Anne Mowbray, Countess of Norfolk (10 December 1472-November 1781). Thus the bride was 5 years, 1 month, and 5 days old and the groom was 4 years, 4 months, and 29 days old.
Thus there are examples of high ranking medieval persons marrying when years younger than the canonical minimum ages.