I do quite a bit of wood finishing and refinishing so I think I have a pretty good idea of what happened; The stain you used reacted to the finish that was on the rocker. That finish was probably what is called in the trade a "combination finish" which is basically a type of quick drying varnish. Oil stain is designed to be applied to raw wood.
Unfortunately, at this point, you have two choices and they aren't good:
1. Strip and start over. There are two ways to strip.1. lots of sandpaper and lots of elbow grease. 2. Chemical strippers.
2. Paint. Some stripping will need to be done to enable the paint to stick. Paint doesn't stick to oil which is what you just applied. If I were doing it, I'd give the chairs a good cleaning with lacquer thinner and denatured alcohol, then I'd sand them thoroughly in two stages. First with 120 grit then 240 grit. I'd use a good primer (Zinsser Bin is my favorite) then apply the color coat of choice.
Also, I avoid those "stains" that they sell at Lowes, Home Depot and the hardware stores at all costs - Minwax being the big name brand. If I want to change the color of a wood, I use a wood dye - which you can not buy at the big box stores or hardware stores. Then I coat that with a sanding sealer - usually good, old fashioned shellac, and then apply several coats of a clear finish. The finish I would use on rocking chairs for a front porch would be McCloskey's marine spar varnish.
I have been using this supply house for decades - head and shoulders above Lowes:
http://www.constantines.com/
I have 3 rocking chairs that I purchased from Cracker Barrel. They needed re-stained so I got a oil based stain that lowes told me to use. I wiped the rocking chairs down with a wet cloth and let them dry. After staining them and letting them dry for about 24 hours they then turned white and very dry feeling. Can someone please tell me what happened? They look worse now than they did before!
