Note that there are more than two possibilities here. You could use "couldn't", "wasn't able to", or "hasn't been able to". The reason "hasn't been able to" is better than either of the other two is that she still can't visit them. The present perfect is generally the correct verb tense to use when you have a condition that extends from the past into the present, and "hasn't been able to" is present perfect, while both "couldn't" and "wasn't able to" are simple past.
In both the sentences:
She couldn't visit them for years, but …
She wasn't able to visit them for years, but …
the word but sets up the expectation that the first clause is no longer true. However, in the sentence
She hasn't been able to visit them for years, but …
this doesn't happen; because you used the present perfect, the listener knows that the first clause is still true, and so is not surprised when the second clause fails to contradict the first.
SUPPLEMENTARY to TRomano's answer.
We use could for general ability. But if you want to say somebody did something in a specific situation, use was/were able to, or managed to (not could).
This does not accurately describe the use of these terms.
Both CAN and BE able to may be used in either present or past tense to designate ‘general ability’:
John {can / is able to} bench-press 300 pounds.
In his prime, John {could / was able to} bench-press 300 pounds.
And both may be used in either present or past tense to designate ability on a specific occasion either at the time you are speaking of or subsequent to that time:
You’re not very well hidden; I {can / am able to} see you! ... The construction with can is if anything a little more likely here.
She wasn’t very well hidden; I {could / was able to} see her.
Dr. Fisher {can / will be able to} see you this afternoon.
She said that Dr. Fisher {could / would be able to } see me that afternoon.
The difference between the two expressions CAN and BE able to arises when we are speaking not of the prospective (forward-looking) ability to do something but of the retrospective (backward-looking) fact of having successfully done something. A past achievement calls for BE able to:
Despite pitching on an ankle that was literally stitched together, Schilling was able to lead the Red Sox past the Yankees and Cardinals to Boston's first championship in 86 years.
As for manage to—this is used only to speak of achievement, not ability. As TRomano says, it emphasizes the fact of overcoming an obstacle.
Best Answer
In this specific case, "can" and "be able to" are interchangeable. But be careful, because there are subtle differences.
For example, your question start with "Can I use..." - this is an example of using "can" with the meaning "is allowed to". Consequently, "can you do it?" may have a very different meaning from "are you able to do it?", and sometimes you should choose your words carefully.