Gearbox shudder and lumpy running on restart

2011 SD4 (automatic) with 94000 on the clock. Recently purchased. FSH, immaculate inside and out. Bit of a shudder at light throttle around 1800rpm as it changes from 3rd to 4th. However when towing a lightweight caravan the shudder is violent and accompanied by a noise like machine gun fire! Also, when restarting the engine when warm it will then occasionally run a little lumpy at tick over and stall when put into gear. Has just had a gearbox fluid flush but problems remain. Any thoughts?

Shudder is normally clutches, which suggests gearbox wear.
I'd exact the box to last longer than 94k, but lack of timely fluid changes is death for these vehicles.
Have you checked the lower engine mount, which are known to fail.

Starting issue could be the throttle body gears beginning to strip.