I practice Autogenic Training, which is a close relative of classic meditation techniques. It is proven to help with anxiety and attention deficit. I don’t know the latter, but I certainly feel the former and I find it easier to not spiral into anxious thoughts.
Keep your promises and be predictable. Predictability and clear rules and consequences create a sense of security and it will make it easier for them to comply. Treat them with respect, they are small, not stupid. Treat them kindly but firmly, what they want isn’t always what they need.
You also might want to talk with the parents about this, they know their kids best and can give specific advice. What works with one kid, might not work with the other.