Bucking While Acceleration and Stuck-off

Might be a hose, might not. Listen under the hood for the sucking sound.

Transmission? Take it to a shop.

There's nothing simple about transmissions. It's most likely crud blocking a port or valve inside.

An easy and accurate way to listen for vacuum leaks is to take a piece of flexible hose cut to about 18" to 24" long. Hold one end of the hose up to your ear and use the other end as a sound probe. Move that end to all the possibly leaking fittings while holding the other end up to your ear and you will be able to hear many more vacuum leaks than just listening with no device. Move it around similar to a stethoscope and if there is a vacuum leak you will find it. Works especially good with the small leaks caused by vacuum leaks in small fittings and hoses.

Good Luck, Old Salt

How long after changing the ignition coils did this start? Are you absolutely sure everything went back where it is supposed to go. Why did you change the ignition coils in the first place? Most cars have just one coil for their entire lifetime, but you chose to change all four of this engine's coils, why? Did any of your old coils test bad? Test any of your new coils test good? Did you test any of these coils for anything?

There you go, I asked six of the twenty questions. Anybody else wants to add a few more? [Oops, that makes seven.]

I agree, it sounds like something not put back together right (if it ain't broke, don't fix it).

Rule #2; The last one that touched it screwed it up.

Does the OP have the 4 or a V6? The V6 has plug wires that are routed under the intake manifold. One coil for 2 plugs. My guess would be a poor connection on one of the coils. Or a vacuum leak. Or a bad plug or plug wire.

I would suggest going back to the old coils, and see what happens. He did save them right?

Bucking on acceleration is common with Pintos, Mustangs, Colts, Broncos and Chargers, and is not unheard of in a Ferrari. Unusual in a Sante Fe, I would agree.

Tell us, is this 'bucking' the reason you changed out the coils?

No wonder why some of them bear horses' breed names, eee haw !!

That post reminds me of that ancient joke(s)

10 year old to another 10 year old:-

"Where are your Bucking ears?"

"Under my Bucking hat!"

Or

5 year old to 5 year old (somewhere in north Yorkshire, UK!):-

"What does your Father call the cat?"

"Cooking Fat - or something like that!"