I saw a few cases here with successful H4 visa. Can we appeal the Consulate for different treatment/discrimination?
-No. There is no law on your appeal basis. The visa officer has the absolute power/right to deny your case with any reason they use.
or it is not smart to do so since we will deal with them anyway in the future.
-Just try the B2 visa again and justify it to the officer that the child needs to live with you (adopted parents) for a few months to build the close relationship between you and your adopted child. This reason is very powerful and I think the VO may consider it.