Indirect realism in perception is the view that we do not experience the world as how it is, but only through and via our interpretations of how the world is. Representation becomes a key feature of Indirect realism. Consider an object 'a,' and let the image of the object that we perceive be, 'b.' Representation is a resemblance relation, that is, if b resembles a (as how the Representational realist wants it to be), then b resembles a.
Representational realism says that image, b, is by definition visible, however the object, a, by definition invisible. How could the resemblance relation hold between something which is visible, and something which is not? This was alluded to me by my mentor, but the original argument comes from George Berkeley.
Putnam's Internal realism, as I understand it, is the view that the world could be causally dependent on the mind and the divisions we find reality, the categories of being is a product of the mind. In this, it is more similar to Kant's Transcendental Idealism where we experience phenomena but are totally locked out from the noumena. Good thing he abandoned it later on! I think, we can run the same argument we did against representational realism against Kant's transcendental idealism. We could argue that as how reality functions, we always perceive things via resemblance relations that ontologically depend on the noumena, and our perceptions follow from them. But that would be too much to go into, however, I suspect you might have the same suspicion as I did when I first ran into these positions. They are both very similar and have very subtle differences, I would argue that the notion of noumena and phenomena, as how Kant puts it, is just as incoherent as Indirect Realism. However the incoherency is not self-evident and would require me to do more work than the question requires me to. If you want to understand more on how both Indirect Realism and Transcendental Idealism could be false, I suggest Searle's Seeing Things As They Are: A theory of Perception, as well as Peter Coffey's Epistemology Part I and II. The arguments for Direct Realism are complex, so it'll be tough reading anyway.