SO what health issues prevent you from vaccinating your dog??
That concerns me most because IF you are going to train your dog to be more social it WILL take being around more kids, people and dogs, and the risk of your dog contracting a disease or passing on a disease is high, and putting an extra liability on things. Next is your dog spay or neutered?

Indeed it is a bit of a precarious circumstance, one that keeps me ever vigilant about their surroundings, but necessary. I have conferred with several vets and the conclusion is the same. One has had hemolytic anemia and just barely survived. Her immune system has never been the same since and the chances of a fatal anaphylactic reaction are high. The other one did have an allergic reaction to her last vac ( at age 6), and again after talking to several vets, the answer was the same. I'm not a fan of over vaccinating, but I do wish my girls could get the rabies shot. They were both rescues that had some health issues when I got them.
And Yes, both spayed.

I can call my dog off any chase with a "leave it".

I might reconsult about her vaccination issues with the vet, if your dog has gotten healthier, she may be able to withstand the injections now, especially if they are spread out over a period of time and not given all at once.
OKAY - prey drive issues. These can be dealt with but you need to be diligent and you should have someone with you to assist you in training.
You need someone with a small dog to walk by you (at a far distance to begin with) the micro second your dog alerts to the other dog, use the command "leave it" a short sharp tug and release on the leash then call her name and have her look at you she should be in a sit stay position.
Now this is all assuming your dog has some basic training under her belt. Also you may want to take her out for a good run or a romp or a swim to wear her out a bit before training starts - a tired dog is much easier to train than a fresh one.
Rhodies have endurance under there skin, so your dog has alot of energy, and this energy NEEDS to be dealt with every day. Your dog should be run or a brisk walk for 2 hours everyday. It does not have to be all at the same time, but 2 45 minute to 60 minute walks are a necessity.
Once you walk your dog start those training sessions.
Your dog should know the basics, sit, stay, leave it. You should have the dog sit before you leash it up, and it should follow you out of the house not leads you anywhere. The dog should be at a heal when you are doing your brisk walk.
Your leave it training sessions should be 15 minutes a day a couple of times a day, the rest of the day you should have your dog by your side, even go so far as to tie the dog to your waist, so it has to follow you around, when you sit, it sits, when you stand it stands, when you you are washing dishes it should be at your side sitting or laying down. Your dog needs to know you are the boss, not it, and part of your dogs training should include it knowing you are the boss.
Let me know how this goes, Im happy to help out

Thank you mazer!! She's an older girl, 9 or 10 and she gets a 30 minute walk every morning. I will see if I can ramp it up a bit on the walk and get another one in the evening, but she does have some arthritis and these days tends to mosey by then end of the 30 minutes.
She does have basic training under her belt, we do training sessions periodically during the week in the evenings and she has down, sit,stay,rollover, shake, leave it etc. Yes, when we leash up, both girls have to sit and I do go out before they do. ( they also have to do various tricks before they get their meals, treats etc.) She walks behind me when we walk but can sometimes get ahead of me when the sharpei gets excited. I have been working with them alot when we pass by the neighbors houses with dogs behind chain link fences. They both have to sit or down until they are calm and then lots of praise when their body posture is good while socializing with neighbor dogs through the fence. We practice the same sit, down stay when we see another dog walking nearby. She gets so focused on the "prey" ( like when we see a cat on walk) that it is hard to snap her out of it. I get her in a sit and will stand to block the view of the cat or other small animal, but I run into trouble trying to snap her out of stalking, even in a sit with me blocking the view. I will have to see if I can find a neighbor/friend with a small dog that would be willing to work with us ( with the distance of course). Thanks so much for the suggestions...

okay it is good to hear she has the basics, let me ask you did this just recently start?? She might not be feeling well because of her srthritis, can she go on meds?? Medcam or even ask the vet about 1/2 a vicodin with a pepcid shooter, it is what I give my dog. He only needs it every other or third day.
Blocking will do no good as you have found out. Not unless you have something your pup wants, a favorite treat or the Natural Balance will work great. Be firm, turn her around if you can. Even a favorite toy can help. It is much like desensitizing training. Basically you are saying yep the prey is over there, I see it you see it, but look at what I got, it is 100 times better.

No, she has been like this pretty much her whole life. The stalking has gotten worse as she has gotten older though. We seem to be managing her arthritis well too with fish oil and Cosequin. For various reasons, I've just not been in the place to specifically address the issue and since so much of the time she has not had the opportunity to stalk. It has always bothered me and now I am in a place where I actively have the time the dedicate to re-training her regarding this.
thanks so much for the direction mazer! I've got my cheese( a bit fav for the girls) with me now on walks and am also taking each dog individually at night to work on specific training issues that each has. Thanks again.

Our male German Shepherd has a strong prey drive. We're having a fence installed in our back yard so he can roam around, but we're worried when the squirrels come to call. He'll go bonkers. We'll probably have to use the electronic collar with the "leave it" command and hope that works.

Trying to train out prey drive is like trying to get people not to breathe. Prey drive is one of the most basic instincts in an animal. We can alter the reproductive drive by neutering. Altering prey drive would require brain surgery.

Instead of trying to train the drive away, redirect the drive.

Provide prey chasing/catching exercises. Like chasing a soccer ball that is kicked. Or a lure thrown. That can be their prey drive alternative, exercising the drive and allowing you to more easily regulate their interaction in other areas because the prey drive has been satisfied.

I do not agree with any of the posting advising that prey drive training is like brain surgery. Given the correct training an owner can train a dog to do amazing things. I just helped my friend teach her service dog to potty on command so she could take him on cruise ships with her. A very basic bodily function....trained in 2 weeks.
If a dog already has a high prey drive an owner would want to start with leave it, and be comfortable with the dog in a sit stay position, not touching a treat or toy before attempting to add anything that moves.