Often writers resort to making characters very stupid and/or suddenly behave uncharacteristically dumb just to drive the plot forward or to force a sequence together, instead of rebuilding or abandoning the idea. "Bagman" is one of those scripts that should've been thrown away early on, but instead they forced through with stupidity. The backbone of the entire movie if made of irrational stupidity. It wouldn't be a movie without it.
I will not list all the times the parents behaved irrational and dumb, but let's say; if you're a normal sane human being with a child who were in danger of being abducted, you would keep it at an arms length 24/7. But no no no. Not these parents. They make sure to always put their kid in danger, giving it away to others and pretty much always make sure to keep it far out of reach and out of sight - just to make this movie possible.
I will not list all the times the parents behaved irrational and dumb, but let's say; if you're a normal sane human being with a child who were in danger of being abducted, you would keep it at an arms length 24/7. But no no no. Not these parents. They make sure to always put their kid in danger, giving it away to others and pretty much always make sure to keep it far out of reach and out of sight - just to make this movie possible.