What kind of wood it it?

What kind of stain?

If there is a chance of lightening the stain, all of the varnish will need to be removed, as the only sure way of lightening stain of which I know is to sand or in some cases use a bleach. But the bleach thing is not a good choice usually.

Sanding oil based stains will remove parts of the stain on close grained woods like maple and pine, but will not remove as much on open grained woods like oak and ash that have lots of depressions sanding does not affect.

Pine often is prone to blotching and uneven staining. So are cherry and maple. A preconditioner is used to even that tendency and reduce the probability. That preconditioner is usually a weak mixture of blond(white) shellac---as that seldom darkens the wood on which it is applied. Oil base conditioners always darken the wood.

Once the stain is to your liking, apply the first coat of varnish with a good manmade bristle brush(I like Purdy brand) and use brushes in the $15 to $25 range. Let that coat dry and hand sand lightly to get the surface smooth---wipe with a lint free rag dampened(not wet) with whatever solvent is used for the varnish---whatever is listed in the instructions for equipment cleanup. Then apply coat #2. Repeat with a 3d coat if needed.

I've done very little work with poplar, but I would be reluctant to stain it- it doesn't have a real clear grain pattern, so will be kind of "flat" when stained. It is known for taking paint very well. Also, the poplar I've worked with tends to be "fuzzy" when sanded. Based on the "one day" application I assume it was a water based "varnish"- which will raise the grain even more. I don't think you are going to be able to lighten the stain- lightly sand with a fine (220 or 300'ish grit ) sandpaper, one more coat of finish, you may or may not need to sand again, then one final coat. You should end up with a smooth finish, however it will still be dark. Hope that helps.

It sounds like he did not sand the wood properly. The courser the grit, the darker and rougher it finish. I am guessing your wood was sanded to 120 grit, maybe less. Also, the rough feeling of the varnish indicates this.

You really need to go to 220 or better, stain and lightly go over it again. I would ask him to replace the trim.

If the sanding was done poorly,you'll get blotchyness in the look of the wood. Finish wise ,I would be concerned about a product that claims you can finish it all in a day.

You need proper drying time between coats AND you need to lightly sand between coats in order to achieve the smooth finish at the end.

My guess is he did NOT sand ( 280 or 320 grit) between coats.

Poplar is not a wood for staining. Sand it and refinish in a nice off-white, or other paint to match your decor. Sorry.