[Galileo1564]

There must be a relation between mass m being affected by gravity and mass m being affected by inertial force.

If mass is connected somehow to space-time and this connection enable mass to curve space-time this connection will also enable space-time to affect motion resulting in inertia .

Yes.

Space-time curvature makes mass to move with acceleration and space-time opposes mass motion with inertia acceleration.

Nothing opposes mass motion. At least that is not the way to think about Newton's 1st, in my opinion. An object in motion will remain in motion and an object at rest will remain at rest, until acted upon by an outside force. When you act upon an object, give it a push or pull, it does what you request. It pushes or pulls based on the amount of force applied. It cooperates. It doesn't oppose.

I think that if you think about it in these terms then you will be able to modify your hypothesis in a more convincing way.

Gravity is a force caused by the gravitational field.
Most pushes and pulls- like me pressing the keys on this keyboard- are caused by an electrostatic field.
There is no real difference.

True.