Can I file a contempt order against him for not reimbursing me for my attorney's fee?
Yes, but before you do, make sure you follow the procedure described here: http://www.divorceinfo.com/enforcement.htm.Will it look bad, on my part, if I ask for reimbursement AND return at a later date asking for child support (via DHR)?
Yes. If you file an enforcement petition, you'll want to include in it ALL the ways he is delinquent so the court deals with all of them at the same time.