Me and my daughter use a tag-along, and her pedals are slippery. So I'm looking for a pair of metal pedals. Due to the axle size, most of them are advertised as BMX, are too wide and long (10x13 or so). Cheap ones (£10) spin poorly. I would appreciate if you could suggest a model or a price range or an ebay/amazon search query that could help me find what I'm searching for.
If you can't find 1/2" pedals then you're looking in the wrong places. They certainly exist but because they're normally a kid's size then quality ones are more unusual.
Check the eco-recycling at the local dump - many kids bikes get chucked out when the child outgrows the bike. Upside, cheap! Downside, they tend to be low quality and have been abused.
Repair the existing pedal - try squirting some penetrating oil/lube into the sides where the pedal body meets the axle. Lay the tagalong on its side to let gravity help. Spin the pedal by hand to help work the oil into the bearing/bushing. Repeat a couple times.
I had some brand new pedals that were rubbish, and ended up spinning them with a 6mm hex bit in a drill press while adding lube. After 10 minutes they got a lot more free.
Make something - if you're competent with tools, consider stripping down the existing pedal and build a new platform. Its absolutely possible to make one from wood, using cartridge bearings at each end of the axle.
Modifying new pedals is possible too - the plastic body is generally adaptable. If its too wide you can file or cut some off.
You can also find adapters to attach 9/16" pedals to your 1/2" cranks. This would give you a much broader selection of pedals to choose from. Since it's your daughter on a tag-along, I wouldn't worry too much about the adapter introducing a bit of weakness to the assembly.