The C-19 stream is the most metal-poor stellar system ever discovered, with a mean metallicity [Fe/H] = -3.38 +/- 0.06. Its low metallicity dispersion (sigma([Fe/H]) < 0.18 at the 95 per cent confidence level) and variations in sodium abundances strongly suggest a globular cluster origin. In this work, we use Very Large Telescope (VLT)/UV-Visual Echelle Spectrograph (UVES) spectra of seven C-19 stars to derive more precise velocity measurements for member stars, and to identify two new members with radial velocities and metallicities consistent with the stream's properties. One of these new member stars is located 30 degrees away from the previously identified body of C-19, implying that the stream is significantly more extended than previously known and that more members likely await discovery. In the main part of C-19, we measure a radial velocity dispersion sigma(v) = 6.2(-1.4)(+2.0) km s(-1) from nine members, and a stream width of 0.56 degrees +/- 0.08 degrees, equivalent to similar to 158 pc at a heliocentric distance of 18 kpc. These confirm that C-19 is comparatively hotter, dynamically, than other known globular cluster streams and shares the properties of faint dwarf galaxy streams. On the other hand, the variations in the Na abundances of the three newly observed bright member stars, the variations in Mg and Al for two of them, and the normal Ba abundance of the one star where it can be measured provide further evidence for a globular cluster origin. The tension between the dynamical and chemical properties of C-19 suggests that its progenitor experienced a complex birth environment or disruption history.