Brake Lever Not Fully Retracting
There are three "parts" or zones to a cable-operated brake.  

1) The hand lever
 2) Inner cable and outer housing
 3) The caliper.

So you released the inner cable from the caliper.  Try pulling the cable through the outer housing and see how much hand pressure you need to apply... it should be relatively minimal.  If you have to get a good grip and pull with shoulder muscles, then the cable is suffering friction with the outer.  

The fix here is to replace both the inner cable and outer housing.

With the cable disconnected, the lever should have tension and pull itself back to the open position without problems.  If it doesn't restore by itself, then it may be corroded, or deformed (ie plastic or metal bent) 

You do say cheapo kids bike which normally means terrible plastic levers and budget stamped metal single-side pull calipers.  Sometimes these just get tired and the spring power is not enough to overcome the resistance from the inner cable.  

Sadly some cheapo bikes are really not worth fixing - you have to make a judgement call.