Dear Friend,
You've not mentioned whether you applied for the new job through proper channel. Since, you mentioned that you want to resign on personal grounds, it implies that you didn't route your application thru proper channel. Had you done so, no appointing authority would hesitate to relieve you for whatever reasons other the ones mentioned in my previous reply. Now, you are caught in between the deep sea and devil - if you officially disclose the reason now you may be in for trouble for violating conduct rules and if you resignation is rejected forthwith, you will lose the new job. Therefore handle the issue tactfully. If the AA is personally known to you and can be taken into confidence, politely explain to him the circumstances in which you failed to observe the rule and appraise upon the better prospects you are going to lose and request an early and peaceful relief.