Lots of ideas. There is no definite answer on this. You don't really know whether she is leaving some urine in her bladder because she didn't empty completely when she went, or whether she is really getting herself properly empty, and the wetness in the diaper is from additional urine being made during the day. It would be helpful if you could figure out which it is.
You might try standing her up, letting her urinate all she can, then wait maybe a minute or so. Stand her up again, see if she would like to empty any more. I do not know if this applies to your dog, but we learned that when expressing the bladder (which you are
not having to do) it is helpful to express-rest-express. During that short rest, the bladder kind of shrinks and reforms itself, and you can get any remaining urine out easier. I do not know if the same principle would apply to a dog that has control, but it would be easy to try.
Another idea might be to use behavior. By that I mean, some dogs will go out in the grass and squat, but then after the first pee, they also go around sniffing every blade of grass and marking various places with a little more. I do not know if she is a marker, but it would be interesting to see if she is inspired to urinate some more during a walk around the yard. Do you have any kind of rear harness to walk her?
Another option would be to let her empty all that she can, then you squeeze her to see if you can express out any more, and by doing that get her completely empty. If you get more out, then you know she isn't completely emptying. If you are not used to expressing, perhaps you could get someone at the vet clinic who is good at expressing to see if they can get any more out of her after she goes.
One more option would be to make her potty breaks more frequent (if your schedule allows it). Different people here have reported that their recovering dog can go different lengths of time without leaking, for example 4 hours, 3 hours, whatever. It might involve diapering her, then checking her diaper every hour to see when it begins to get wet.
There are some medications that are useful in elderly female dogs who wet the bed. One is Proin, another is DES. Sometimes they are used in combination. There may be something newer they are using now, my experience is over 10 years ago. I do not know if they would be applicable to your dog, but in senior female dogs that develop incontinence with old age, they can help prevent leaking. You would just want to be careful that you do not try any medication that is going to hinder her ability to urinate independently like she is doing. It might be something to ask the vet.
I kind of replied about the neurologist in the other post. If you can afford the neurology consult, that would be nice. I think a physical therapist might also be able to give you an evaluation of the movement in the leg, and the status of the other leg.
Silly me, but what color of poodle is she....?