"When an upperclass single mom gets her baby kidnapped by it's father, she has to enter the dark forest and hunt the vicious hunter down to get her baby back."

I see.

If this is set in present day what is stopping the mother from alerting the authorities? Surely the police could help.

Perhaps leverage modern medical technology and state that the child is in need of dialysis and have them live in a remote village. Then even if the police rush over it could be too late so the mother has to pursue the father herself to save the child.

MC is easy to empathize with the goal is clear the stakes are clear and the antagonist has clear motivations. However I would sharpen the pencil by adding to the stakes.

Describe the father in a way that would put the child at risk; could the father be a hunter gone mad, a paranoid psychotic or convicted for murder?

Might even want to give it a ticking time bomb by making the child need regular medication. Could the child be a diabetic, asthmatic, or have a heart condition? If the MC doesn’t save the child in time he or she could die either from their health or from the father.

This also very quickly made me think of this story as set in mid 19th century Europe. Did you have a specific time and place in mind?

Hope this helps.