You would of course change your child's status to H4, as this is a better status than TD in terms of GC process.
Your
TN status is tricky, in that once you submit I-485 (which would be submitted either in conjunction with, or slightly after your spouse would file her I-485) you will no longer be able to renew TN, or enter US on existing TN.
This situation is analogous to the one where YOU, the TN holder, would be directly applying for GC. In such cases, the TN-holder ensures that they have sufficient time remaining on TN (typically 5-6 months) before filieng I-485, and they file I-765 and I-131 at same time, and remain in US, working in TN status, until they I-765 (EAD) and I-131 (AP) are approved before venturing outside US.
You will then switch your work authorization to the EAD, and make sure you keep the EAD and AP current (ie. renewed before expiry).
The only wrinkle in your situation is that your wife MUST inform her firm's lawyer that you are on TN, and that before filing I-485 for you, that you have taken care of your TN timing issues.
It isn't so critical that your child do anything right now, so long as at some point before his I-485 is filed, he switch to H4.
But, be assured, that one can indeed migrate from TN to EAD to GC, so long as one remembers to have sufficient TN time remaining in order to stay i nUS and In TN status during the 4-5 months it takes to get EAD and AP approved. One does not have to go directly from TN to GC.
-- Wed Jan 06, 2010 3:49 pm --
... and just to clarify, each person applies for GC individually: your wife's firm sponsors her, and simultaneously, her dependants apply based on her GC process.