  Laser wakefield acceleration is paving the way for the next generation of
electron accelerators, for their own sake and as radiation sources. A
controllable dual-wake injection scheme is put forward here to generate an
ultrashort triplet electron bunch with high brightness and high polarization,
employing a radially polarized laser as a driver. We find that the dual wakes
can be driven by both transverse and longitudinal components of the laser field
in the quasi-blowout regime, sustaining the laser-modulated wakefield which
facilitates the sub-cycle and transversely-split injection of the triplet
bunch. {Polarization of the triplet bunch can be highly preserved due to the
laser-assisted collective spin precession and the non-canceled transverse
spins. In our three-dimensional particle-in-cell simulations, the triplet
electron bunch, with duration about $500$ as, six-dimensional brightness
exceeding $10^{14}$ A/m$^2$/0.1$\%$ and polarization over $80\%$, can be
generated using a few-terawatt laser}. Such an electron bunch could play an
essential role in many applications, such as ultrafast imaging, nuclear
structure and high-energy physics studies, and the operation of coherent
radiation sources.
