My impression is that glaucoma (which is, basically, too high intraocular pressure) is easy to diagnose. Two doctors disagreeing on it would worry me.
Don't get just a third independent opinion, get a fourth one as well.
It was less than a disagreement. I'm sorry that I over-emphasized this point. The first time the pressure was Hgmm 26/18, the second time 19/17. The second doctor said that the pressure can fluctuate, and her equipment is not enough to settle the question. (She is an I-don't-know-the-correct-term national health service doctor, the first one is an expensive private doctor with better equipment, and more time for a patient.)
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.