Answer:
Yes, It is vital that the court gets the correct information to solve the case otherwise the outcome could be wrong. Even if it means testifying against someone you love.
If the Relative is your spouse you do not have to testify against them,
In the law of the United States, the spousal privilege comprises two separate privileges, the marital confidences privilege and the spousal testimonial privilege.
The marital confidences privilege (or marital communications privilege) is a form of privileged communication protecting the contents of confidential communications between a married couple. This privilege applies in civil and criminal cases. When applied, a court may not compel one spouse to testify against the other concerning confidential communications made during marriage.
The spousal testimonial privilege (or spousal immunity) can be used to prevent any party in a criminal case from calling the defendant's spouse to testify against the defendant about any topic. In federal court as a matter of common law, this privilege attaches to the witness spouse; that is, the defendant's spouse can refuse to testify against the defendant, but the defendant may not prevent his or her spouse from testifying against the defendant.
This privilege does not survive the marriage; that is, after divorce, there is no right to refuse to testify against a defendant ex-spouse.
Anyone can refuse to testify in court by pleading that by doing so they believe they may incriminate themselves along with the defendant,the 5th amendment of the US Constitution firmly states that you have the right not to incriminate yourself. This is what it means when people say they "plead the fifth".
If your testimony would not be incriminating to you and you just don't want to testify against a family member you can Refuse to do so in any court in the US. However by refusing to give testimony to the court the judge may charge you with contempt of court and you could be fined and/or jailed.This rarely happens if the proceedings are of a civil nature,such as smail claims court or other civil court proceedings and even trafic court..It mostly occurs in criminal court proceedings,and Family court proceedings dealing with divorce or child custody.