You broke what I consider to be the first rule of finishing... you didn't do any samples of the entire finish before you started on the actual project. The chair and table bottoms are a good place to test the steps of your finish to make sure it's going to come out the way you want it to. But you're in good company. Lots of other people have done the same thing. There's a couple previous discussions on staining parawood at these links;
The simplest fix, if it works to your liking, is to sand the poly with 220 until it's dull and then use a thick stain (e.g., gel stain) as a glaze. Once the finish is dull, remove the dust and wipe on a thin coat of the glaze. It will help to even out and darken the color. It's not a perfect fix, but may be good enough to avoid a complete refinish job. Once the stain/glaze dries for a day or more, you can apply a couple more coats of poly varnish over it for protection. Follow the manufacturer's guidelines for applying the poly. If the poly smears the stain/glaze, give it more drying time.
Test the glaze on the bottom of a chair seat or two. If that looks good, try one whole chair from start to end. If that looks good, do the rest of the pieces. If the glaze isn't working as well as you'd like, stripping and starting over is an option, but a LOT of work. A paint and varnish remover from a local paint or hardware store will do the job of removing the poly and a lot of the stain. You'll have to do a lot of sanding to remove enough stain to get the color even.
If you do remove the finish, start with one chair and do everything from start to end on it before tackling the rest of the pieces. Strip the old finish, sand out the stain, sand very well up to 180 or 220 grit to prepare it for the new finish, and then apply the new finish. First, try the entire new finish on the bottom of the chair seat (or the bottom of the table) to see how it looks.