  The discovery of magic-angle twisted trilayer graphene (tTLG) adds a new
twist to the family of graphene moir\'e. The additional graphene layer unlocks
a series of intriguing properties in the superconducting phase, such as the
violation of Pauli limit and re-entrant superconductivity at large in-plane
magnetic field. In this work, we integrate magic-angle tTLG into a double-layer
structure to study the superconducting phase. Utilizing proximity screening
from the adjacent metallic layer, we examine the stability of the
superconducting phase and demonstrate that Coulomb repulsion competes against
the mechanism underlying Cooper pairing. Furthermore, we use a combination of
transport and thermodynamic measurements to probe the isospin order, which
points towards a spin-polarized and valley-unpolarized isospin configuration at
half moir\'e filling, and for the nearby fermi surface. Our findings provide
important constraints for theoretical models aiming to understand the nature of
superconductivity. A possible scenario is that electron-phonon coupling
stabilizes a superconducting phase with a spin-triplet, valley singlet order
parameter.
