We theoretically model the spin-orbit interaction in silicon quantum dot devices, relevant for quantum computation and spintronics. Our model is based on a modified effective mass approach which properly accounts for spin-valley boundary conditions, derived from the interface symmetry, and should have applicability for other heterostructures. We show how the valley-dependent interface-induced spin-orbit 2D (3D) interaction, under the presence of an electric field that is perpendicular to the interface, leads to a g-factor renormalization in the two lowest valley states of a silicon quantum dot. These g-factors can change with electric field in opposite direction when intervalley spin-flip tunneling is favored over intravalley processes, explaining recent experimental results. We show that the quantum dot level structure makes only negligible higher order effects to the g-factor. We calculate the g-factor as a function of the magnetic field direction, which is sensitive to the interface symmetry. We identify spin-qubit dephasing sweet spots at certain directions of the magnetic field, where the g-factor renormalization is zeroed: these include perpendicular to the interface magnetic field, and also in-plane directions, the latter being defined by the interface-induced spin-orbit constants. The g-factor dependence on electric field opens the possibility for fast all-electric manipulation of an encoded, few electron spin qubit, without the need of a nanomagnet or a nuclear spin-background. Our approach of an almost fully analytic theory allows for a deeper physical understanding of the importance of spin-orbit coupling to silicon spin qubits.