Should I e- file with the dependents that haven't been rejected and then mail in an amended form along with proof I can file the one that was rejected? Or mail it all in?

[Critter]

Option B ... mail it all in. 

[fanfare]

when claiming a dependent you do not attach any statements of "proof" (evidence).

Just put that away for the day that IRS asks you to present it.

Sending an amendment just makes extra work for you and the IRS and causes more delay.