We present seeing-limited (0.8″) near-infrared integral field spectroscopy data of the type-2 quasars, QSO2s, SDSS J135646.10+102609.0 (J1356) and SDSS J143029.89+133912.1 (J1430, the Teacup), both belonging to the Quasar Feedback, QSOFEED, sample. The nuclear K-band spectra (1.95–2.45 μm) of these radio-quiet QSO2s reveal several H2 emission lines, indicative of the presence of a warm molecular gas reservoir (T ≥ 1000 K). We measure nuclear masses of MH2 = 5.9, 4.1, and 1.5 × 103 M⊙ in the inner 0.8″ diameter region of the Teacup (∼1.3 kpc), J1356 north (J1356N), and south nuclei (∼1.8 kpc), respectively. The total warm H2 mass budget is ∼4.5 × 104 M⊙ in the Teacup and ∼1.3 × 104 M⊙ in J1356N, implying warm-to-cold molecular gas ratios of 10‑6. The warm molecular gas kinematics, traced with the H21-0S(1) and S(2) emission lines, is consistent with that of the cold molecular phase, traced by ALMA CO emission at higher angular resolution (0.2″ and 0.6″). In J1430, we detect the blue- and red-shifted sides of a compact warm molecular outflow extending up to 1.9 kpc and with velocities of 450 km s‑1. In J1356 only the red-shifted side is detected, with a radius of up to 2.0 kpc and velocity of 370 km s‑1. The outflow masses are 2.6 and 1.5 × 103 M⊙ for the Teacup and J1356N, and the warm-to-cold gas ratios in the outflows are 0.8 and 1 × 10‑4, implying that the cold molecular phase dominates the mass budget. We measure warm molecular mass outflow rates of 6.2 and 2.9 × 10‑4 M⊙ yr‑1 for the Teacup and J1356N, which are approximately 0.001% of the total mass outflow rate (ionized + cold and warm molecular). We find an enhancement of velocity dispersion in the H21-0S(1) residual dispersion map of the Teacup, both along and perpendicular to the compact radio jet direction. This enhanced turbulence can be reproduced by simulations of jet-ISM interactions.