Any amount that you gift that is less than the annual exclusion is not counted toward the one million lifetime total of gifts that the gift tax
is not due upon.
So, the gifts of 20,000 to each child is not part of the one million.
Also, you could gift $13,000 on or after January 1, 2009 to each child each year and not count that amount toward the one million lifetime amount.
You and your spouse are each each entitled to the annual exclusion amount on the gift so together you can give $26,000 after January 1, 2009 to each child each year.
You are correct that the one million is all that one person can give without paying gift tax so that it would be 500,000 each for two children. Your spouse also can gift property she owns up to one million in her lifetime without paying gift tax.
Other than the requirement to file and pay the gift tax on Form 709 the only tax consequence is that the child will then on be the owner and have to report any income from the partnership.
for links to the forms and instructions.
You should consider consulting an experienced tax practitioner so that the gift of the interest in the family limited partnership can be accurately reported and any possible discount to the value (such as due to lack of marketability) can be applied. Valuations will need to be competently performed by well qualified experts.
I hope this helps for the general rules
for gift taxes.