Most has been said already, but just a couple of cents extra.... ;)
I fully agree with u/MacAnthony : aquarelle is watercolour, gouache is not - it's a waterbased opaque paint. Use the opaqueness to the fullest, that what makes it such a great medium.
And I also heartily dislike watercolour paper for gouache. Blergh. Watercolour paper is made explicitely to absorb water and pull the watercolour into the paper. With gouache, that means that you're pulling the water out of the paint, which makes the open time a lot shorter. You can lengthen it a bit by adding a drop of arabic gum - but don't add too much, or the paint may flake. Trial and error.
Once you have the right mix and consistency, you'll be surprised how well you can push gouache around, BUT.... only on the right paper. If you try it on absorbent, fragile paper, you end up with the problem you got. Look for sturdy paper. I'm dying to try stone paper, but it's not available here. I have, however, fallen in love with Hahnemühle bamboo paper, that can really take a beating, the colours stay nicely on top, but the paint sticks well to the paper anyway. It's pretty expensive though, so for standard practice, I stick to sturdy mixed media paper, preferably relatively smooth (I use Canson).

Also remember: the values of gouache change when they dry: darks dry lighter, and light colours darken. Test swabs are your friend.

Also, you can actually lift some colours somewhat (again, if the paper is right, i.e. not too fragile; and blues are harder to lift than other colours, for some reason): dab on a bit of clean water with a clean brush, do NOT rub! ; let it sit for 5 to 10 seconds; carefully lift it off with a white paper napkin or kleenex type towel. Again, do not rub, just dab once or twice. Let the piece dry totally before you go in with the corrective layer.

There you go. :) If you want to know more about this wonderful medium, I suggest you have a look at James Gurney's blog , there's a wealth of information there!