Assuming there is nothing obviously wrong, the next thing we check is that the load rules are correct and that the tag is supposed to be firing. This is often the cause for this kind of live/qa site difference - a load rule being set to a specific live-site URL, for example.
Next it's a matter of looking in either the network tab of developer tools, or the sources tab (if you are using Chrome) to see if that particular tag is being loaded.
If you would like us to take a look, please feel free to send an email through to firstname.lastname@example.org with the details.
Yes, you'll be able to refer to it via the 'b' object.
If you've mapped it then you can refer to the mapped name by u.data.[name].
e.g. if you may 'example_data_source' to 'test' then you could refer to it as 'b.example_data_source' or 'u.data.test'
Mapping to in custom containers is very powerful. You might want to read this post to learn a bit more about the power of custom containers: