Thanks for all your comments above! At least I know there are people out there sharing the same pain. I talked my husband into painting these built-in bookcases white instead of staining so they would match other white trimming, when he was skeptical about the brush marks and imperfections with painting wood. I promised to find a high quality paint for a professional look and thought I did when my research turned up so many people raving about ProClassic, including this one: http://www.centsationalgirl.com/2012/02/pedestal-table-with-overlays/
They made it sound so user-friendly and I believed.
I think I'm going to wait a few weeks and ask my carpenter to sand it. If we can get it back to a smooth surface, we'll use the roll and brush technique as you guys recommended and also described in this earlier post:
"I roll a line of paint down the length of the cabinet about 4-5" wide (about the width of the mini-roller), then go up and down a few times with the roller to make sure the area is fully covered. Then take your brush (the first time, get a little bit of paint on the end of the brush but not too much-a totally dry brush gums up a bit) and go from top to bottom or bottom to top once or twice at the most). Keep a very light touch with the brush and try to hold it more parallel to the surface than perpendicular. Then reload the roller and roll another strip, slightly overlapping the previous one, then brush. Continue until finished.
When dry, lightly sand with 220 grit, wipe clean and apply another coat. It goes very quickly. Just don't take a break until you've fully finished your surface because you want to keep a wet edge."
BTW, is this the correct 4" roller to us? http://www.homedepot.com/p/Wooster-Pro-4-in-x-1-2-in-High-Density-Woven-Fabric-Roller-Cover-0HR2780040/204354021
If we want to skip the brushing, would rolling alone almost always cause orange peel?
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https://www.dhgate.com/product/european-full-copper-toilet-paper-holder/404368651.html#s1-5-7b;searl|2942913402
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