Bummer! I second Alloy's suggestion of a professional repair, if you want to do it yourself I'd use a piece of Eternabond roof repair tape. The Barker tote is made out of polyethylene and after cleaning the area with Acetone, Eternabond will bond to it.
A split seam is the same as a crack in the surrounding plastic, so the fix is the same. First thing is to drill a hole at each end of the split to relieve the tearing stress. Otherwise the crack will keep on spreading,
If it's a short tear, that may be enough to make the tank mechanically stable and you can apply the Eternabond. If it's a long split, you may want to make a reinforcing patch out of sheet metal, then drill and pop rivet it in place to provide mechanical strength before applying the Eternabond.
I haven't had much luck welding thin plastic. The temperature has to be just right ... too cold and the weld breaks off, too hot and the underlying plastic melts and you wind up with a larger hole or a thin spot.