Short answer: the problem is caused by your behavior, not by the dog.
- He goes with the dogwalker without any notable problems.
- He always went with you (without your husband).
- He also went with your husband when you felt ill.
- Now he won't walk without both of you.
The question is: What does the dogwalker do differently? What did you do in the time since he would walk with just one person to now?
My assumption is: too much coaxing. You turn the normal situation of walking with just one human into something "special", probably even something "scary" that is to be avoided. This is a pattern that is very common and causes problems for a very long time without the owners even realizing:
- You go on your usual walk.
- One of you has to leave early. Of course the dog notices this and reacts to it. He looks after the departing human. One part of this is the dog caring for his owners, but the other part is communicating with the remaining human. Did you notice that? What do you do? What should I do?
- You react to his behavior and talk to him, probably telling him that everything is ok and that he should continue walking. He cannot understand a single word of what you say, but he understands that you also react to the situation. The nonverbal communication your dog understands is: this is not normal, you should react to this.
- The dog reacts even more to the same situation the next time it occurs, and you coax him even more, ending in a vicious cycle when the dog refuses to walk unless both his humans are nearby.
The dog walker doesn't have time to coax every single dog away from home, so he never entered the vicious circle. The dog knows that the walker will take him away from home for a while and that that is ok (because the walker doesn't react to his worries and treats the situation just like something normal).
The way out of this situation can be a very long one, or it can be quick and easy, depending on the dog and your behavior. I would try the more extreme changes first, in hopes of "resetting" his behavior and solving the problem quickly. More gradual changes will need more time to take effect.
Drastically change his "going for a walk" routine:
Go at a different time than usual. You can try a collar if he usually has a halter and vice versa. If you have several doors, leave the house through a different door than usual. If you always turn right at the first corner on your walk, turn left instead and take a different route.
And most importantly: treat the situation like the most boring, normal thing there is. You can tell your dog "this way", but don't coax him at all. You are the one on the walk and he has to follow you.
This drastic change can get some dogs so puzzled they forget their habits and ingrained routines, which gives you the chance of a new start. Other dogs might become too insecure and refuse to leave the house for a new reason. Don't push this approach if it doesn't work.
You didn't specify how exactly your dog refuses to walk with only one human, but a common reaction is for the dog to stand or lay in one spot and not moving a step forward until the human caves in and returns home. Pulling the leash in that situation doesn't change a single thing, because the dog still doesn't take a step. You can drag him over the sidewalk without him moving a single paw.
Even lifting him up and carrying him won't change a thing. The dog refuses to walk and he still isn't walking if you carry him.
Dogs are pack animals, so they have many gestures to communicate with their pack members. You can adopt this language to speak with him in terms he understands much better than human language.
Face your body the way you want to go. Turn only your head and look at your dog. Call him to you while walking into the intended direction.
Don't exert a constant pull on the leash. Give him a short pull on the leash and then immediately release the tension again to tell him he's supposed to move. It's important that you don't pull so much that you cause your dog pain. If you cause him pain, he'll hate walking even more than he does now.
Another solution is to gently nudge or push your dog forwards. When he stops, keep the leash taught so he cannot run backwards, but move towards him and if possible behind him. Then push his hips or his flank forwards into the direction you were walking. This is more likely to force him to actually move his legs and walk with you. Once he's moving, continue your walk forwards as if nothing ever happens.
Be stern, but reward him for obedience
If you regularly do obedience training with him (which you should), you should be able to call him to you on command. If you cannot reliably recall him at home, this solution has no chance of working for you, but you can spend a week or two to train his recallability at home and on the walk.
Take some of his usual treats with you on a walk and recall him in very regular intervals, not just when he refuses to walk. If he starts refusing to walk, call him to you. Don't negotiate by being to soft, repeating the command too often or coaxing him. Be stern, call him to you, reward him. As long as he doesn't move, you don't move. The only way he is going home is after he came to you and got rewarded.
Training a completely different thing like "stay" or "down" with him can also work by distracting him from his stubbornness and putting his head into a different mode. See the second linked video at the bottom for an example.
Treat walking alone as normal
If you can't bring him to walk with only one person, start your walk together. Sometime during the walk, you stop and Person A says goodbye to Person B in a swift and happy manner, but not to the dog. Person A turns around and walks home without turning back. (This is important because turning back is nonverbal communication meaning follow me.) Just a few seconds after Person A leaving, Person B continues the walk and calls he dog to them (like a short "come on").
Threat the experience like the most normal situation of all times. Don't negotiate with your dog, just continue your walk. You can employ some of the other mentioned methods (like gently shoving or recalling him) in combination with this.
Alleviate his fear
If he is actually anxious (shivering, tail low or between his legs, ears hanging low, making puppy eyes at you) you can alleviate his fear by simply crouching down with your legs slightly spread. This creates some kind of living shelter where many dogs love to receive support and comfort.
Do not crouch down right next to him, your goal is still to get him moving on his own volition. So do it a few steps away and let him come to you, but only if he actually shows signs of anxiety.
These suggestions are a summary of my own experiences and advice you can find on the internet, like