Just to be clear you are getting a shudder in second gear or in first gear shifting into second?
I suspect you are dealing with the most common issue with this transmission and that is the forward clutch pack is burnt up. This will cause a variety of issues but it will cause shudder in second going to 3rd.
Take a look at this video that illustrates this perfectly:
Even if you don't have an issue with the 3-4 solenoid, I still suspect you have burnt clutch material which is causing the shudder. The only way to know this at this point is to take it apart and replace the clutches, steels, pistons, and seals. Basically you will want to just rebuild the unit to ensure you only go into it one time.
Let me know if I misunderstood something and we can go from there. Thanks
Images (Click to enlarge)
Sunday, April 26th, 2020 AT 4:53 PM