How do you effect change in a Rat Terrier?

Someone who is experienced with Labs may have more to offer, but I'll share some input from a having multiple dogs in the home perspective.

Feed and give treats to the dogs separately, in their own spaces (either different rooms or introducing a crate and making it a small cozy den where the rat terrier will feel safe - a soft fluffy liner/blanket & giving treats there may help). I'd also suggest separating them whenever nobody is around to ensure peace is being kept (i.e. during your husband's long work days). Even dogs that are best friends can injure each other accidentally during play or unintentionally when reacting to stimulus, such as a delivery, mail, etc.

The fact that it usually takes two people to contain a squirmy little dog at the vet doesn't concern me. However, the fact that the rat terrier bit them (after getting acquainted over 3 visits) does cause some alarm. I would enlist the vet as your ally and seek their opinion. They have a huge frame of reference for normal behavior, by breed/age/situation and likely can provide resources if you open up conversation (i.e. do they recommend any specific trainers who use positive training techniques, are there other potential reasons/medical factors why the dog bit, why does he tremble, what do they suggest).

Until some of this behavior gets resolved, it would be simpler to just make the bed a dog free zone. That way he doesn't think he's protecting you or the territory and try to nip your husband if he approaches.

The Lab guarding resources (possibly stealing a treat, who knows if that's the only thing that has transpired in your absence) and playing aggressively doesn't make it sound like the best fit. Both of them may benefit from implementing new rules.