You can make a hotkey for a bandolier change, and you can sort of make a hotkey for an item click if the item is in a worn slot or a top level inventory slot, but you can't hotkey an item click from inside a bag, or integrate an item click into a social hotkey line. The bandolier window has a "Hotkey" button on it to make one automatically, and there is also a "/band activate NAME" command for it that you can put into social lines. There is no way to make one social hotkey that both selects a bandolier line *and* clicks an item. An item hotkey is a thing unto itself that can't be integrated into other socials in any way at this time.
Which part doesn't work in the above? Unfortunately they changed the range on "/target" a couple years back to be fairly close, so now you'd need to be almost on top of the pet to have it work. Also, while the previous poster said to use "/cast haste", what they meant was "/cast 8" where the 8 is the spell gem number (1-10) where you have haste loaded. If the haste spell isn't memorized then it won't just find it in your spellbook and load it for you. You could also set up a spell set to simply load haste in a specific spell spot and put that into another hotkey, but obviously the time frame to memorize and refresh a spell defeats the purpose of combining into this hotkey to hit an RS pet in the relatively short period it is up.
Oh, I think see the problem. EQ has a funny habit of using a "back tick" instead of an apostrophe for things like "Yitamin`s pet". It will depend on your keyboard, but the "back tick" is located on the same key as the tilde (` ~) on most Western/English keyboards I think. Usually it is located on the top row of numbers, to the left of the One key (! 1), just under the Esc key.