Start off by going for a ride where you can safely drop the lead rope and not worry about the second horse.

If things get exciting, drop the lead and focus on controlling the horse you are on.  I have one gelding that is the alpha for my herd.  He will gare and kick at horses that try to pass him  or get too close on the trail. So I had to work on his manners.

The are two issue that you will have to deal with.

1st is manners. teaching the horse that you are the boss and if you choose to have a second horse that close, He needs to respect your decision and tolerate that second horse being close. Make sure you have a calm down queue that you can give while holding a lead rope in one hand. Some of the old cowboys I know roll their spurs on both sides which they have taught means, lower your head and relax. Others shake the reins etc. Just realize one hand will be committed to the lead rope, So what ever you use as that queue needs to be done with out that hand.

2nd,  is al the new things that are going to happen. Lead ropes get under tails. under stirrups, they slap him on his hip as you ride. The led horse may stop and bach at a stream crossing. This may cause you to change your balance as you get stretched between a horse moving and one stopped. If any of these really upset the horse you are ridding, just drop the lead rope, settle the horse you are one and go back and collect the lead.

Do your intial rides at a walk. I find my horses get more worried about the second horse the faster I go. They want more space at a trot than at a walk. So until everybody is comfortable, stay slower.

Like anything, it just takes some time and wet saddle blankets. They will come to understand and be comfortable with the process. I do this with all my babies,  I start taking 6 month old colts out along side their mares. When they become yearling and two year olds, I take them alongside what ever horse I'm riding.  It lets me get two horses exercised in one ride. The babies learn all about trails long before I start to ride them. They cross creeks, over bridges, they learn to step up over ledges or blow down trees. Early in their saddle careers, I will start to pack them. Saddle with panners and some light camp gear. They get used to stuff floppin around. By time I actually start to ride them, they are not worried about saddles , gear, obsticles, they just need to learn to balance a rider.

My daughter really likes to ride my gelding that likes to kick.  She watches him and when she see him flatten his ears back. She knows thats the sign he's getting ready to let the other horse have it.  My daughter boxes his ears when she see them flatten. It takes his attention away from the other horse and seems to work to control him. 

You may want to see if there is a pre sign when she starts getting witchy. Then do something to get her attention back on you and not worry about the other horse.

It sounds to me like you have two problems to fix and neither one is gong to allow you solve the other.

To answer your question, you can't safely pony a horse with your "Ms. Congeniality".  You must first fix her issue or your other horse will never muscle up because your mount is going to hurt either you, your other horse or both.  You must have a dead broke absolutly trustworthy mount to pony with.  By dead broke I mean "will not do anything unless I tell you" broke. 

If you have any apprehensions when you saddle up to do your conditioning exercise, you are not doing it safely.  Sorry. 

We have friends that lead every trail ride.  They had a prior horse that just followed (very cool)  so we have asked and learned a few pointers.  The big trick we learned from them was two extra knots evenly spaced in the 6 foot standard lead line.  You use these knots (which you adjust to the leadee over time) to slip thru or gather up.  We were shown never let the led horse get in front and never let him fall behind. 

Our reason for all this was to get our retired horse out for some trails.  The main issue he had was he is our fastest horse and after a few miles he is all done being asked to hold back.

So we only treat him to this occasionally.

I can't tell you how many miles I've lead a 2nd or 3rd horse. But some how they figure it out with practice.  yes I've dropped the lead rope a few times . when the pack horse has gone around the wrong side of the tree, or refused to cross a blow down while my lead horse continues to move, or when teaching a new lead horse not to worry about ropes under it's tail. You drop the rope, circle back and pick it up and continue.

Anytime the horse I'm riding threatens the ponied horse, I get after the lead horse. Give them something to do Before they can act up and kick or bite. Half halts, side pass, lateral gives, something to get their attention on me and forget about the second horse.

Even my youngest daughter has learned to pony a second horse. And the sorrel in this pictures likes to kick other horses. But they learn to deal with it.

Like PaintedHorse says, it just takes wet saddle blankets and a smidgen of common sense on the rider's part. Horses are like kindergarteners on the playground. They fight and bicker with each other until you give them something else to think about. You are likely to have a few mishaps along the way, but most of these will be more of a nuisance that a danger. 

Marla