Can eternal inflation and gravity explain dark energy?
We need to cover some basic concepts: inflation in our universe ended 13 billion years ago. Inflation occurred for just a short period of time after the big bang. Eternal inflation is different. It hypothesises that spacetime is infinite and keeps on inflating. In some regions of spacetime, the inflation stops and the energy from this inflation is converted into energy and matter. This region where inflation stopped becomes sort of like a 'bubble' in the ever inflating spacetime. This bubble is then a universe. This there can be multiple universes accelerating to this hypothesis.
Okay. Our current theory of gravity is General Relativity, and for now all you need to know is that it seats that gratuity thanks time to propogate and has only a finite reach unlike Newton's description of gravity.
So even if our neighboring galaxies have a slightly different observable universe, the gravity from galaxies far apart don't even affecter them at all. In fact, that is why or universe is expansion by without any noticable obstruction from gravity.
Gravity takes time to propagate and has a limited access, so far away galaxies don't even affecter each other. That is why expansion is actually happening.
Another thing is I think your understanding of dark energy is somewhat misleading. You say that dark energy pushes the universe from the inside. That is the exclamation it the universe. The expansion does not happen because of dark energy. Dark energy accelerates the expansion. We have observed that expansion of the universe is getting faster and faster as time passes. For this you need energy. That energy is dark energy, failed so because we haven't detected it yet.