Are your kids natively Spanish-speakers?

If so, saying "use a letter "T" sound simply may not work. A Spanish "T" is more of a "dhey" then it is a "tee" sound (in phonetics). It's softer, farther back on the palate, and slower.

If they're native Spanish speakers, they see a written "Too" and they default to playing with a "dhoo" which makes articulation sound mushy or thick, as you state. Work to force a truly English sounding "T" sound in your articulation. Make it aggressive. Stay on it.

That being said, if you're having some of the other issues you've described, make sure they're breathing together, starting the air stream with the tongue, and not locking/closing the throat.