"That" part in a game

For QTE's, I do have quick reaction speeds, so as long as what I'm supposed to do gets to me, I can do it quite well. The motion controls thing on the other hand can be a bit mixed. Sometimes I have no idea what the motion controls are because I don't read the instruction manual, & even when I do figure it out, sometimes the game in question may have bad detection of them, which is especially common in cases like Wii shovelware, clones of it such as the Wireless 60 or MiWi(the console that led to a Vinesauce segment called Plug and Plague) & the infamous Kinect. Either that or the controls are a bit too complex & ambitious for motion controls for me to get the hang of. Or both, both is especially painful.

Are there "arcade stick" controllers for PS2 (I've definitely seen ones for PS1, however)? 
For my favourite game, The Dog Island, for the Wii version you still have to shake the remote in order to dig things up but thankfully it doesn't require precision. Instead of having to move the pawprint cursor I just press the d-pad (rotate camera) to change direction while holding B (run). With Okami I thought it would be easier to play on Wii than PS2 because the Wii remote can be used single-handed, but I'm stuck in the first location because I can't do the motion to make Amaterasu jump.
I love the Trauma Center series for DS and Wii but the time limits and precision required makes it too difficult for me even on easy mode, so I get more enjoyment by watching playthroughs.
The Dora the Explorer games for Wii & PS2 have a copilot mode but only because of being intended for young children (this was before systemwide options were a thing).
I have several games for this console; because it's meant for toddlers the buttons are nice and big so it's useable with minimal motorcontrol.

Pretty much ANYTHING stealthy for me. Whether it's in Final Fantasy, Sly Cooper, Ghost Trick, Spyro the Dragon, Zelda: Ocarina of Time, Spongebob Squarepants: Battle for Bikini Bottom, etc. I'm 100% gonna SUCK at it. It's the main reason I have been too skittish to ever try a Metal Gear Solid game no matter how much they fascinate me on a lore level :/

death egg zone in sonic 2

Just about any stage from Bubsy 1 past the carnival stages are very annoying to me with their frustrating level design, bad controls & physics combing together.

king of the pile from rabbids go home

Yeah, those sound like they can be hard as heck & not all that fun.