One of the slave-concubines permitted... Could someone explain what this sentence means please [closed]

Solution 1:

It's saying that if one of the slave-concubines bore a child from a member of the royal family then that child would not be considered an heir to the royal family. They can bear a child, but the child would not be a "Royal Successor", ie could not succeed to the throne. The child would be a "bastard", to use the old terminology, who were not considered as legitimate heirs.

https://en.wikipedia.org/wiki/Bastard_(law_of_England_and_Wales)

"Intrigues", in this context, means "things which happen that are not made public but may be of interest to some people, or manipulated by people for their own ends". See the noun definitions here:

http://www.dictionary.com/browse/intrigue

In this case it's referring to the love affair between a member of the royal family and a concubine, and probably also various ways in which certain parties tried to exploit this for their own ends, make accusations, etc.

Solution 2:

One of the slave-concubines permitted my father

"One of the slave-concubines" is the subject of the sentence whose verb is "could…" while "permitted my father" is a participial phrase modifying "one of the slave-concubines". The "my father" is a retained object from a ditransitive sentence which would look similar to:

(Someone) permitted my father slave-concubines~.

This is in active voice, but in passive voice, it would look like:

Slave-concubines~ were permitted my father by (someone).

In your sentence, "by (someone)" is omitted.