HELP PLEASE! I introduced 1 new bird into the mix...not going well.

hello everyone.
I am new to this forum and new to raising chickens. I need some solid advice about flock behavior/pecking order and what to do.
here is the situation.
I started with four chickens (1 leg horn, 2 Rhode Island Red, 1 Wynadotte). My babysitter left the door to the backyard open and my dog killed 2 of the chickens (1 rhode island and the Wynodotte). major trauma to everyone involved (except the dog). many lessons learned (not looking for advice on this). The 2 remaining chickens started laying again and are acting normal.
I decided to introduce another bird into the mix about a week ago. A 3 month old Buff Cochin. At first we separated them in the coop and who put the new lady in with them at night. When they are all in the pen together, the Rhode Island attacks the Cochin. The leg horn has joined in as well. We continue to separate them during the day. We are currently trying to get the Leghorn and Cochin to get along as the Leghorn is less aggressive when the Rhode Island is not around. This is going fairly well but the Cochin just looks nervous all day long and is very skittish.
I feel like i made a mistake in introducing only one bird...
How to I amend the situation?
How long does it take to establish a pecking order?
Should I get another bird to balance things out?
I am worried about my Cochin as she usually hides under a log for most of the day.
Please help!
thank you!
Jeanette

You should always try to introduce 2 (preferably 3) or more birds at a time, just for moral/flock support among the newcomers. In your case, keep the cochin in a pen (like a dog crate or some other sort of secure area) where it has its own food/water/shelter but is visible to the other two. Let them like that for 2-3 weeks or so so that they can all get used to each other's presence without being a direct threat to anyone. After that, start trying to free range them together (or set them all loose in the run together if you don't free range) SUPERVISED. They might go at it for a bit, but give them a few minutes and see what happens. If blood is drawn and it doesn't let up, back to the visible quarantine for awhile. Be patient and keep trying.

At this point, if you add a new bird, it's just going to be a stranger to the cochin AND the other two and you'll cause even more drama. I'd avoid that for the moment. Pecking orders can take a few seconds to a few weeks to establish and are ever subject to changes.