what is the verbal phrase in this sentence?

Victoria taught Priscilla to swim with the family dogs.

Is it to swim with the family dogs or just to swim?

In this sentence, what is the verbal phrase?
He decided to follow Carol and the pig into the deep water.

Is it to follow or to follow Carol?

The infinitive phrase is "to swim with the family dogs."

http://www.chompchomp.com/terms/infinitivephrase.htm

to follow Carol

In this sentence I believe the verbal phrase is sinking fast

Unfortunately, Anthony felt himself sinking fast.

Is sinking fast a participial phrase or a gerund phrase due to the preposition?

Sinking fast is a participial phrase.

The only preposition in this sentence is "in."

In the sentence "Victoria taught Priscilla to swim with the family dogs," the verbal phrase is "to swim with the family dogs." The entire phrase functions as the direct object of the verb "taught."

In the sentence "He decided to follow Carol and the pig into the deep water," the verbal phrase is "to follow Carol and the pig." The entire phrase functions as the direct object of the verb "decided."