You were promoted based on your qualifacations and experience,you were promoted because your boss felt you were the best person for the job.
There is probably a little bit of sour grapes going on.
Be confident in your position,you deserve it.
If you need to take disciplinary action then do.
This is not a playground this is work,if the staff don't realise this perhaps a gentle reminder that there are laws against bullying in the workplace.
Lead by example.
You could call a meeting,state what your new role is and what is entails.
Management Skills
The link above is about management skills,perhaps you may be able to implement some of the tips.
To end, if your not happy in your new role and if its affecting your health then by all means talk to your boss,but keep in mind the attitudes of your staff may not change should you demote.