I am actually surprised whatever allegations have not been already prosecuted since Spanish libel law is very strict, as it is in Europe in general. Unlike the US, where it is only a matter for the civil court, under Spanish law, it is a matter of penal law. In that case, it wouldn't be the royal family suing, but the prosecutor bringing charges. So why haven't they?

Here is a summary of the law: defamation constitutes a criminal act, known as “calumny” and “injury” under Articles 205 and 216 of the Penal Code. In Spain, 'calumny' is a crime by spreading or publishing a falsehood when you either know it is not true, or with 'reckless' contempt of the truth.

Specifically:

The Spanish Criminal Code includes two general types of offences against honour: slander (Art. 205) and defamation (Art. 208).

Slander (Criminal Code Art. 205; calumnia): Defined as “accusing another person of a felony while knowing it is false or recklessly disregarding the truth”. It is generally punished with a fine of six to 12 months. However, when committed by means of the media (print and broadcasting) or other “similarly effective means”, it is punished with a fine of 12 to 24 months or imprisonment for up to two years.

Defamation (Criminal Code Art. 208; injuria): Defined as any accusation, expression, or action that “harms the dignity of another person, detracting from his reputation or attacking his self-esteem”. Defamation is only considered a crime if “by its nature, effect, or circumstances is considered serious by the public at large”. In the case of an assertion of fact, the offender must also know the statement to be false or have acted with reckless disregard for the truth. Defamation is generally punished with a fine of three to seven months. However, if the defamation is committed through the media, the potential punishment increases to a fine of six to 14 months.

In certain cases (e.g. if defamation was committed for payment), the offender may be barred from certain rights, such as holding public office or practicing a particular profession (Art. 213, in accordance with Arts. 42-45) for six months to two years.

Finally, Art. 620 of the Criminal Code provides that defamatory statements that do not otherwise constitute a felony are considered a misdemeanour (falta) and punishable by a fine of 10 to 20 days.

Art. 578 of the Spanish Criminal Code prohibits “acts that involve discredit, disdain or humiliation of the victims of terrorist offences or their relatives”. The penalty is imprisonment from one to two years and a fine of 12 to 18 months. Art. 578(2) stipulates that penalties shall be on the higher end of the spectrum if the act is committed through the media or the Internet.

I don't think the king or queen have the right to tell the prosecutor not to proceed with charges, so why aren't they doing anything?

Personally, I don't think any monarchy is in any danger to fall because of such allegations. If it were to do so, that would mean it is shaky in the first place, and then, all sort of constitutional issues would be at play.