How did European royalty respond to domestic violence? Also what would be the reaction of it becomes common knowledge and I don't intervene
It's a little earlier than 1000, but we do hear about a case similar to your question in the sixth-century Histories by Gregory, bishop of Tours. Gregory wrote about the deeds of the Merovingian ruling dynasty, which included quite a bit of violence, including significant violence against women. Violence overall, including domestic abuse, was probably far more normalized in sixth-century Frankish society, given the casual nature with which it is often discussed, but that doesn't mean it was always condoned, or that violence could be enacted against royal women without consequences. However, the tale of Galswinth in Book 4 of Gregory's text suggests that diplomacy may have outweighed concerns about a woman's safety in her marriage.
In the text, Gregory tells us that Chilperic, the Merovingian king of Neustria, sends a message to the king of "Spain" asking for the hand of his daughter in marriage. The king sends his daughter Galswinth to marry Chilperic in 556. But, Chilperic, contrary to the agreement, refuses to send away his mistress, an enslaved woman named Fredegund. Offended at sharing her husband with a woman of lower status, Galswinth asks to be allowed to return to Spain (Greg. Tur. HF IV 28). In response, Gregory writes that Galswinth is strangled in her chambers, most likely at the command of her husband. Chilperic then marries Fredegund, his mistress, some days later. His actions are met with only mild reproach by Chilperic’s own brothers, who use the killing as a failed excuse to challenge him. Perhaps more surprisingly, Galswinth’s family in Spain makes no recorded response.
In this case, Galswinth's distance from her family might play a role in the lack of consequences following her murder - because she leaves her family, and has no male relatives close by to support her, there is little anyone can do to protect her. Janet Nelson (6–7) argues that a foreign queen’s “rootlessness” might afford her the advantage of greater physical freedom and political maneuver as compared to her husband, but it also posed significant dangers should she suddenly find herself unwanted. After her death, there is clearly not a politically sound reason for the Spanish royal family to seek revenge against Chilperic or the kingdom of Neustria - they do not choose to use the event as an excuse to wage war, which they very well could have. So, although this example is earlier than your question, it does demonstrate that even royal women could face abuse and even death without their kin making any response, if the politics were not in her favor.
Sources
Gregory of Tours, Libri historiarum X, edited by Bruno Krusch and Wilhelm Levison, MGH, SRM, vol. I.1. Hannover: Hahn, 1951.
Nelson, Janet L. “The Wary Widow.” In Property and Power in the Early Middle Ages, edited by Wendy Davies and Paul Fouracre. Cambridge: Cambridge University Press, 1995.
astereris answer reminds me of a similar situation. I've edit this a bit form my 2am original reply.
The Danish king Kristian II had a mistress he cared for a lot, Dyveke, with whom he spent a lot of his youth. The king later married Elisabeth (Isabel) of Austria. Her parents were king/queen Philip/Joanna of Spain, grandfather Maximilian I Holy Roman Emperor and her brothers later became Charles V and Ferdinand I, Holy Roman Emperors. The wedding took place in 1515, the bride was 14 and the groom 34. Everyone expected the king to give up his mistress, as was customary, she'd be "pensioned off" and likely married to a loyal retainer. That's how it was done.
Kristian II would have none of that though. He had read his Machiavelli (probably not), and acted accordingly. He kept his mistress, whom he considered an important advisor as well as lover, along with the mother-in-mistress Sigbrit, who also was important as an advisor and later effectively worked as finance minister (if that had been a thing then) for the king. They were put up in a house in the capital some distance from the palace. Naturally everyone thought this was, mildly put, in poor taste if not an outright scandal. Dyveke and Sigbrit were foreigners (Dutch) and even worse, commoners. The nobility were largely outraged.
The queen, insulted, complained to her family (it was an insult to them to), Maximillian I Holy Roman Emperor, possibly the most powerful entity in Europe at the time. Other than reproaching his grand-son-in-law the Emperor could or would do little (that and not paying the dowry, though that wasn't paid in full until Charles V was emperor anyway). Nor could anyone else, noble or high clergy alike (both groups already in conflict with the king). Maybe. Dyveke died suddenly in 1517 and talk of assassination circulated, the more famous story is poisoned cherries. The king was enraged and had some people he held responsible executed, among them a high-ranking noble. Effectively driving a wedge between the king and his important nobility. Spoiler, this is going to come back and bite him.
While Denmark-Norway +- Sweden (still technically part of the Kalmar Union though effectively at this point independent), was one of the largest countries in Europe by area, if not by population and economic might, the HRE was mightier yet. Yet neither Maximilian I nor later Charles V could really impose their will on their wayward grandson/brother-in-law.
So what do learn from this? (Unlike Kristian II who later became known as Kristian Tyrant after he first won then lost Sweden and was deposed by his nobility and replaced by his uncle, told you it would end badly, and we are skipping several massacres because they aren't important here.)
Likely you care about your sister, but that's not a given. Does "care" mean you'll go to war? Probably not. War is expensive. Even the power of the HRE did not do that against an important, but distinctly 2nd tier country. If you were going to go to war anyway? Well, then God just handed you a just cause most will accept.
You'd be expected to intervene, in a manner of speaking. You'd likely be using your influence in subtler ways. But it should be noted you are not the only one expected to intercede. While during the period a husband of any sorts had the right to chastise his wife, laws and common customs did tend to provide a limit on what you could do before society around you started reacting. Legality aside. Depending on time and place family honour mattered, as naturally did your own. Abusing women didn't show your strength, rather it weakened your honour in the eyes of others. So most likely we fall back on familial ties, clerical influence[rs], politicking nobility, and all kinds of (underhand) influence. Even the general view of the common people matters (a little). Threaten to support rivals and shelter their enemies. Have bishops or the Pope (jackpot!) censor the offender. There are a lot of "soft power" options like this. One Swedish king formally challenged a Danish king to a duel to settle a war (it didn't happen but resulted in an impressive Danish diplomatic snark comeback).
There are many ways to peddle influence, and reputation is important for everyone, even kings. You are only as powerful as your allies/rivals will let you be. If you hurt your prestige as ruler people will chip away at your powerbase. Enough of undermining can topple you and earn you a not-so-cool nickname as did happen to Kristian Tyrant. Though he wasn't a wife-beater as such.
Oh and there's always poisoned cherries, never forget the poisoned cherries.
You could also look at Henry VIII of England and his Great Matter (tm) to see how the influence peddling happens. Again not necessarily in a direct abuse situation though certainly Katherine's reputation was abused and this would at time be equal if not worse then physical abuse.
Sources am picking for stuff about Kristian II:
and on the legal/societal issues for women during the period:
and yes, full disclosure I had to check wikipedia to make sure names and dates were correct while writing this up