Q: Ignition Coil/Prak Plug Issue

So my girlfriend left work yesterday and as she began to drive her engine light turned on followed by your EPC light.

She felt the car vibrating and even shaking. She mentioned that it would get more violent as she accelerated and that she felt a slight loss of power.

She took it into a mechanic that night and dropped it off. The mechanic called her back and said that it is a Ignition Coil issue and that two coils are failing. They said it would cost upwards of $850 to fix the issue.

Now I know that it shouldn't cost that much for coils and spark plugs if they are needed. I looked it up and coils from the dealership are about 38 dollars and spark plugs are 15. Ive watched a few videos and it seems like a really simple swapping of parts.

I went into the mechanic shop myself to try to get her car and they wouldn't let us take the car. they said we would ruin it and a bunch of other things.

i'd like to know if this diagnosis is correct and if i should make the fix myself? thanku

My car has 70000 miles.
My car has an automatic transmission.