I have 2008 Ram Bighorn and over the weekend When it shifts into OD it feels like it is lugging or shuddering. Anybody know what might be the problem?

My 03 did that a few years back. I can't specify details as to what happened but I ended up getting it rebuilt. Sit down when they give you a quote...

What is the difference between TOWING mode and OD off. When I push the button one time on the end of my shifter it shows TOWING and when I push it again it shows OD off. In TOWING mode the RPMs are about the same as regular and the (vibration or slight shuddering stops). And when I push the button the second time it cuts the OD off and the RPMs go up and the issue also stops. Is it the lock up converter causing the problem?

Towing mode or OD off turns off your MDS so it drives on all 8 cylinders all the time. You might have a MDS problem and not a trans problem?

I had an 08 Ram for a few years and I didn't think the MDS did much for mileage in my commute. 11 miles one way half city half highway. I drove it a week in Tow/Haul mode so it would not have MDS and my mileage didn't suffer.

2008 Ram is not much information to go on. What engine, what trans, 1500, 2500, 3500, 2 or 4WD?

2008 5.7 Ram Bighorn 1500, 2 wheel drive. If it is the MDS what can I do to fix it.

Guessing there are no codes since you did not mention it...

Checked the fluid lately?

Ultimately might need to take it somewhere or find someone with a scan tool to take it for a ride.

Intake has to come off to get to the MDS. Those solenoids can get stuck. AMHIK.

At the dealer I used to work at before I retired we had a tool called a Co-Pilot and also the Tech Tool lab top could record the electronics with both. I would have a tech drive it with you in it also to give his opinion and record it because if it is a missfire from the MDS or anything else they should be able to see it in the 02 reading and addaptive fuel. And they can also see if it is the torque converter shudder as I said in your other post. Even some independent shops may be able to record the electronics like the dealer can and it may help find the problem.
I remember once I had a Caravan that would start bucking about 50 mph and do it real bad and I only found the problem when I recorded the electronics and then downloaded it in the shop diagnostic computer. It had a bad speed sensor that right about 50 mph the reading would jump to over 500 mph and as high as 504 mph. Well the PCM kills the injectors on that model at 118 mph and the PCM thought it was going over 500 mph and would shut off injectors. That Co-pilot or any recording device is a good tool as many things happen to fast for a tech to see on a scanner while driving. Good luck , Ron

As much information as they are running through those computers, one would think they could program into the computer that the vehicle isn't capable of going 500 mph. Especially a Caravan! Gene