  We consider a non-Abelian dark SU(2)$_{\rm D}$ model where the dark sector
couples to the Standard Model (SM) through a Higgs portal. We investigate two
different scenarios of the dark sector scalars with $Z_2$ symmetry, with Higgs
portal interactions that can introduce mixing between the SM Higgs boson and
the SM singlet scalars in the dark sector. We utilize the existing collider
results of the Higgs signal rate, direct heavy Higgs searches, and electroweak
precision observables to constrain the model parameters. The
$\text{SU(2)}_{\text{D}}$ partially breaks into $\text{U(1)}_{\text{D}}$ gauge
group by the scalar sector. The resulting two stable massive dark gauge bosons
and pseudo-Goldstone bosons can be viable cold dark matter candidates, while
the massless gauge boson from the unbroken $\text{U(1)}_{\text{D}}$ subgroup is
a dark radiation and can introduce long-range attractive dark matter (DM)
self-interaction, which can alleviate the small-scale structure issues. We
study in detail the pattern of strong first-order phase transition and
gravitational wave (GW) production triggered by the dark sector symmetry
breaking, and further evaluate the signal-to-noise ratio for several proposed
space interferometer missions. We conclude that the rich physics in the dark
sector may be observable with the current and future measurements at colliders,
DM experiments, and GW interferometers.
