I would be very careful about adding sand to 'dense' soil as that can often result in exactly the opposite of what you're trying to achieve. If you decide to go that route, I would strongly recommend using a test plot before amending your entire garden.
It's difficult to make a recommendation based on the information available, but gypsum (often sold cheaply as 'soil conditioner' but check ingredients) could be your answer. Even if it doesn't solve your problem, it won't cause any harm.
Beyond that, the default response to most soil woes is, "Add organic matter." Peat can be useful, but be aware that it is acidic and will likely lower your pH.
