is this sentence a gerund (if not can i fix it to be a gerund)-. The children despise being disconnected from the nursery the primary source of the cruel experiences.

I would say that "being disconnected from the nursery" is the gerund phrase. The word "being" is the gerund itself.

A gerund is a noun formed from a verb. Remember, unlike other nouns, a gerund can take an object.
I like swimming.
I like swimming the lake.
[swimming is the gerund]