Use whatever feels right. You don't even need to swish it around - it will do its absorption thing just being there. You're right that if you spit it out after swishing instead of ingesting that it's not as constipating.
How often you do it depends on how much detox you're looking for. Usually when you start ingesting clay the first thing you'll notice is an amazing clarity with your thinking. Guess it makes sense given how many toxins in the environment that affect the brain and nervous system.
I haven't tried diatomaceous earth, but I keep meaning to. Silica is seriously good stuff.