Is this sentence transitive Sally is very patient with her pesky little brother?

No, the sentence "Sally is very patient with her pesky little brother" is intransitive.

Here's why:

* Transitive verbs require a direct object, something that receives the action of the verb.

* Intransitive verbs do not require a direct object.

In this sentence, "is" is the verb, and it expresses a state of being (being patient). It's not acting on a direct object. "Patient" describes Sally, and "with her pesky little brother" tells us *about* her patience, but it's not something she's *doing* to her brother.