No, you don't buy clothes for kids in Sims 3. I think you can direct them to use the dresser or use the command, editsim, in the cheat window while your child is selected. That should take your Sim to CAS where you can create up to 3 outfits per category for that Sim.
As for the other problem, that is how Sims 3 works. You create a family and plop them on a lot, then you create another family and plop them on a different lot. You lose the progress your first family made - wishes, career promotions, just about everything.
If you don't want to lose everything you worked for with your first family, you might want to look at Pescado's
awesome mod. The mod contains many new features and fixes to allow players to play Sims 3 the way they want to. Read up on the description, features and installation instructions carefully.