I'll just chime in to say that in my opinion, the employer had two pertinent facts to deal with:
1. OP made it clear that work would be second priority to the kid's activities. Fine, that's his or her choice to make, but it's not the first thing an employer wants to hear.
2. Asking to reschedule a drug test is probably a big red flag. The employer could have a policy that anyone who doesn't take the test when scheduled doesn't get hired.
Bottom line, if you aren't going to meet the commitment you make before you even start the job, the potential employer sees it as a sign of things to come if they hire you. Offer withdrawn.