HSA catch up contribution if both myself and my wife are 55+

Both myself and my wife are 55+.  So, I think each of us can contribute an additional $1000 on top of the limit. We do have 2 HSA accounts, one for my wife and one for myself plus my kid.  My question is whether the above mentioned understanding is correct.  Also, when filing tax, the total contribution for the family will be $2000 more than the regular HSA limit for family.  Will that be a problem?