I think I have researchet all the available options in Denmark, a variety of trailers and three-wheeler ladcykler (cargo bikes).
We have about 5000 kr (about 700€) to buy for, and we do at the moment only have one bike, that we both share.
So we need a new bicycle + a trailer (either crappy chinese bike + medium quality trailer - or medium quality bike + crappy supermarket trailer), OR a ladcykel, which in Denmark almost inevitably is a trike.
Pro: Cheap, light, you don't have to ride around with it all day, but can leave it at the daycare.
Con: The child is far behind you, difficult to communicate with the child and solve minor problems fast, the risk of cardrivers not seeing the trailer (despite the flag),
Pro: Very roomy, space for several playmates/lots of cargo.
Con: Heavy, difficult to manouvre, price way above our budget.
But then I came across the two-wheeler cargo bike, a Long John type of child (and cargo) transporter. Very interesting and maybe the one to solve our problem: Bakfiets Cargobike Long. But we still only have 5000 kr. So what to do? Well, on this market too, you can find a cheap (chinese) model. The quality is probably as low as the price. I found this online shop: http://www.bakfietsweb.nl/product.php?t=nl&model_id=15 (and tricycleweb.nl and ladcyclerweb.nl).
Edit: We ended up buying a Chariot Carriers child transportation system, model Corsaire. High quality and within our budget.
(By the way, we wasn't sure whether to buy Corsaire or Captain. The only difference between them, is that the Captain has a molded plastic bottom (great for heavy wear, rough terrain/stupid car drivers and being used every single day), and the Corsaire has "just" the "plastic fabric" (but that is very sturdy too).
We bought the latter because it is slightly smaller (a 2 kg lighter), and thus would easier fit in the boot of a small car).