2006 Mercedes ML500 Shudder/Tremor

Hello! I had some work done at the local dealership, but I still have the same shudder during acceleration issue. (And, the stereo wouldn't work.) 230k miles. 5.0L V8 automatic

I told the dealership, "I have an acceleration issue. It seems like somewhere between 2nd and 3rd gear or 3rd and 4th gear, there's a shudder while accelerating. It's fine at highway speeds and fine at lower, neighborhood speeds. But, in between, it shudders and stalls." They had it for weeks. When I picked it up, they said they test-drove it fine for 30 miles. 3000$, couldn't even make it across town. Had to tow it home.

I'm not sure if I said the wrong word/words to describe the issue, if it's a known issue, or if I was just taken for a ride. But, after fuses and relays, both batteries and the mass airflow sensor (and filters) were all replaced, I got it running again.

After getting it home 1) it used to idle for 10 (9:55) minutes and just shut off. Read: limp mode 2) auxiliary battery was draining main but couldn't hold charge past 1 volt. Replaced. 3) strangely, after replacing both batteries, the stereo worked for about 20 seconds. Display works, but again no sound/volume. 4) check engine light came back after reconnecting new batteries.

So, now it runs. I reversed up my driveway about 100 yards and drove back down to my parking spot 3 times. No issues. Quickly got up into 4th gear on the 3rd run. Felt confident to take out to the road.

Didn't go more than 200 yards, driving normally (rather conservatively), and the shudder/tremor was back. Reversed back home. No smoke. No weird noises. Parked.

Open to suggestions. Please help. Thanks in advance.