Althought this probably belongs in another forum (woodworking), I have found that sanding teak is difficult (just to get it right). My problems did not include staining, but I can see how staining teak can be problematic (people online call it waxy; I suppose that's the closest word). The act of sanding and resanding teak is has left me with the opinion that planing-only is preferable to sanding (teak). Regarding steel wool, I've tried it and found issues. I met a guy who used it, but the stuff he made wasn't so great.
But, regarding stain, was the teak bleached first? Some manufacturers bleach teak with the intention of staining it, and then there's the sun, which can also weather any wood. Whenever I have used teak I simply went for the natural finish, so you'll have to consider my advice about staining with the knowledge that I know about staining in general. Teak purportedly doesn't absorb stain well (I can believe it), but there are many factors in play, like grain (cut of the wood), or whether this was previously finished and then sanded (such that the finish was not fully removed).
In essence I do think that re-sanding could be necessary... and uneven sanding might be required for an "even" stain. Don't think about this like a machine; think like a painter painting a picture. Another possibility for what might have went wrong is that the stain itself was not fully mixed when the staining began. If this was the problem then you should be able to darken the lighter areas with more stain (unless you have already varnished the lighter areas). Yes, mineral spirits can still be helpful for removing excess stain, but it could also be harmful. Again, think like a painter, and take your time.
There might be a simpler option, though. Generally, stain will spread a little more, soak in, and blend in after a couple of weeks. I know that you said it has dried but for how long? Of course, doing nothing requires patience. I wasn't watching when you first started, so I can't really say if the first part of the railing has just faded a little. If you can wait, you should take before and after pictures- with some swatches in the photo, next to the railing- so that you can monitor it. If you are seeing the darker areas fading, then just keep waiting it will probably work out.
