I can't say for sure, but I think there are some clues in The Clone Wars episode "Voices" when Yoda contacts the Force Ghost of Qui-Gon Jinn. Qui-Gon says that he is a "manifestation" of the Force, and explains that the Force is made up of two parts, the "Living Force" and the "Cosmic Force". From the transcript here:
I am a manifestation of the Force, a Force that consists of two parts. Living beings generate the Living Force, which in turn powers the wellspring that is the Cosmic Force. ... All energy from the Living Force from all things that have ever lived, feeds into the Cosmic Force, binding everything and communicating to us through the midi-chlorians.
In the old expanded universe there was a similar distinction between the Living Force (a term which Qui-Gon used in The Phantom Menace) and the Unifying Force; the wookieepedia article on The Unifying Force is rather misleading IMO because it relies too much on a single EU source (Jedi Academy Training Manual) that described these two as fundamentally different schools of thought about the Force, but as discussed in this article, this source was inconsistent with many other EU sources that discussed the Living and Unifying Force as two different aspects of the Force which were both accepted by Jedi, more similar to Qui-Gon's discussion. A more typical explanation of the distinction is this one from The Jedi Path: A Manual for Students of the Force:
The Force is bigger than all of us, but expresses itself in two aspects. The Living Force is raw and close at hand. It is the life energy tingling around you when you pass among plants and animals in a walk through the jungle. When beings die, you sense it through the Living Force. When many die at once, the loss of their energy may shock you, even knock you out. All of your tangible Force abilities—such as running, jumping, heightened senses, moving objects, or soothing the emotions of others—are techniques by which we become agents of the Living Force.
The Unifying Force is a vast cosmic power. You may not sense it yet, but with patience and insight you will. The Unifying Force is the stars and galaxies, the rippling surface of space and time. It is this voice that whispers of your destiny, and make no mistake—the Force does have a will. To commune with the Unifying Force is to temporarily leave your body, allowing you to walk in the past or see the future. Some of the ancients believe it is even possible to transcend death.
So basically, the Living Force is more about the present moment, the "raw and close at hand", while the Unifying Force is more about "destiny" and knowledge of the "past and future". Although the Unifying Force wasn't directly mentioned in The Phantom Menace, this sort of distinction involving two aspects of the Force, an unnamed one dealing with the future and the Living Force dealing with the present, was suggested by this dialogue:
Qui-Gon: Don't center on your anxieties, Obi-Wan. Keep your concentration here and now where it belongs.
Obi-Wan: But Master Yoda says I should be mindful of the future...
Qui-Gon: ...but not at the expense of the moment. Be mindful of the living Force, my young Padawan.
The wookieepedia article mentions that the first appearance of the "Unifying Force" was in the novelization of The Phantom Menace, you can see on p. 141 on google books that it distinguishes the two in a similar way:
The Force was rooted in the balance of all things, and every movement within its flow risked an upsetting of that balance. A Jedi sought to keep the balance in place, to move in concert to its pace and will. But the Force existed on more than one plane, and achieving mastery of its multiple passages was a lifetime's work. Or more. He knew his own weakness. He was too close to the life Force when he should have been more attentive to the unifying Force. He found himself reaching out to the creatures of the present, to those living in the here and now. He had less regard for the past or the future, to the creatures that had or would occupy those times and spaces.
Terry Brooks, who wrote the novelization, consulted with George Lucas on it (discussed on p. 142-143 of Brooks' book Sometimes the Magic Works, which you can read if you use the 'Look Inside' feature on amazon by clicking the image of the cover, and then search for the keyword 'Lucas'), so it seems likely that such a basic revelation about the nature of the Force would have come from Lucas or at least have been approved by him. And Lucas was heavily involved in story planning for all the episodes of The Clone Wars, so it seems likely that when he introduced the distinction between the Living Force and the Cosmic Force in "Voices", the basic idea was supposed to be similar to the Living and Unifying Force distinction.
So, this background knowledge should help in interpreting this later exchange between Yoda and the Force Ghost of Qui-Gon in "Voices":
Yoda: See the future, you can?
Qui-Gon Jinn: I exist where there is no future or past.
Yoda: Know you who the Sith Lord is?
Qui-Gon Jinn: I can only show you a place where the answers will be revealed to you.
"No future or past" would seem to suggest that when Qui-Gon said earlier he was a "manifestation" of the Force, that he was in some sense speaking for the Cosmic Force dealing with destiny--my speculation would be that while he retained his individual personality to some degree, there was no longer really a distinction between his will and the "will of the Force" (which might sound too anthropomorphic, but Qui-Gon himself used the phrase in The Phantom Menace, saying to the Jedi Council that 'Finding him [Anakin] was the will of the Force'). And I think this is also suggested by the fact that instead of answering Yoda's question directly as a normal flesh-and-blood Jedi would presumably do when asked an important question by another Jedi, he said "I can only show you" the place where Yoda would go on to have a Force vision, revealing information in the somewhat mysterious and indirect way that Jedi always received information from the Force. And note that although Yoda did learn some things about Sidious in this and the followup episodes, he never learned the crucial information that Sidious was Palpatine--presumably it wasn't part of the Jedi's destiny to learn this until it was too late.
A lack of distinction between the will of a Force Ghost and the will of the Force overall (the destiny 'assigned' by the Cosmic Force) is also suggested by some dialogue Yoda and Qui-Gon had in the original script of Revenge of the Sith (written by George Lucas), though it didn't make it into the final cut:
QUI -GON: (V.O.) Patience. You will have time. I did not. When I became one with the Force I made a great discovery. With my training, you will be able to merge with the Force at will. Your physical self will fade away, but you will still retain your consciousness. You will become more powerful than any Sith.
YODA: Eternal consciousness.
QUI-GON: (V.O.) The ability to defy oblivion can be achieved, but only for oneself. It was accomplished by a Shaman of the Whills. It is a state acquired through compassion, not greed.
YODA: . . . to become one with the Force, and influence still have . . . A power greater than all, it is.
QUI-GON: (V.O.) You will learn to let go of everything. No attachment, no thought of self. No physical self.
Becoming "one with the Force" but still being able to "retain your consciousness" might seem like a contradiction, but I think it would make sense if the oneness was in terms of a loss of distinction between personal will and the will of the Force, which would also fit with the idea of "no attachment, no thought of self".
So, my answer to your question "are the Force Ghosts able to interact with the real world whenever they want to or whenever the Force allows them to do so?" is that I think there is no longer any distinction between what the Force Ghost might "want" and what the Force itself would "want", the Force Ghosts only want to take actions in the world whenever these actions align with the "will of the Force" or destiny (which on a meta level is just a way of saying they don't do things that would screw up the broad story Lucas wants to tell, like Anakin falling to the dark side and the Empire temporarily victorious until Luke claims his destiny as a Jedi), and don't want to otherwise so there is no need for the Force to not "allow" them to.