What should I do about and old DUI that I never showed up to my court date for?

I think that the best thing for you to do is to go and hire an attorney as soon as you possibly can for all of these matters.  These are very serious issues here and you need to deal with them head on and right away, especially with a small child at home. Your arrest three years after the failure to appear at the DUI court date, was that for an outstanding warrant issued from the original charge?  You are making things so much worse for yourself and really they could be cleared up with very little effort.  You appears to have cleaned up your act and gotten a job and are raising a family and not to have been rearrested except for the warrant.  Please hire an attorney and deal with the matter now.  Good luck.