<p>We theoretically study the enhancement of quantum entanglement in a hybrid electro-optomechanical system consisting of a main optomechanical cavity and an auxiliary optical cavity. The two optical modes are coupled through photon-hopping interaction, whereas the two nanomechanical oscillators, by means of tunable Coulomb interaction. An optical parametric amplifier is also provided in the auxiliary cavity for nonlinear gain and phase control. We solve the linearized quantum Langevin equations and use the formalism of covariance matrix to quantify bipartite entanglement between different subsystems using logarithmic negativity. According to our results, the photon-hopping coupling indeed enhances the entanglement between these mechanical oscillators and makes it more resistant against thermal-decoherence so that this entanglement persists up to higher temperatures. We prove that the Coulomb interaction is a necessary condition for mechanical entanglement in which its strength <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\lambda \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation> determines how correlated the system becomes. Additionally, we show that the optical parametric amplifier is a powerful tool for phase-sensitive boosting of mechanical entanglement as well as crucially enabling entanglement between the two optical modes which would otherwise be missing. However, this improvement is compensated by the shrinking of the stable parameters region. This work provides a general and flexible approach towards the manipulation of quantum correlations via the interplay between Coulomb interaction, photon hopping, and parametric amplification with applications in quantum information processing and sensing.</p>