Learn English – Flee from vs flee

SHORT ANSWER:
From here is formally incorrect. What NPR should have said is:

... she robs that child of the ability to feel good ...

LONG ANSWER:
Rob is an odd fish; it ordinarily takes at most one complement, but that complement may be either of two entities.

In its oldest (and still primary) sense, it means “deprive someone unlawfully”, and its complement is the victim—the person or institution against whom the offense is committed:

Dick Turpin and ‘Captain’ Tom King robbed virtually everyone who passed their hiding place.
Willie Sutton robbed banks “because that’s where the money is”.

In this sense, the goods taken are expressed in a preposition phrase headed by of:

Footpads robbed him of £24 and his watch.

Quite early, however (OED 1’ earliest citation is 1377), the word was occasionally extended to the sense “take by robbery”, with the complement expressing the goods taken. In this case the victim is expressed in a preposition phrase headed by from:

The gang robbed more than a thousand dollars from passers-by.

But this use has never been common, and it should certainly be avoided in formal contexts.

However, rob may also be used intransitively with the meaning “commit the offense of robbery”, and in this sense the from clause to express the victim is proper:

He robbed from the rich and gave to the poor.

run away or flee sounds like something that refugees do: it's not something that you would want to associate with a paradise resort.

escape is probably a good word to use about the daily routine. It suggests freedom, which is a positive idea. get away is similar.

There is a significant difference between get away and run away, as explained here

I would recommend using escape for the first clause, then something different, also with positive connotations, in the second clause.

escape from daily routine and visit/come to/find sanctuary in our paradise resort.