GUI is supposed to slide from the side on touch?

Improvements

You can get smooth motion with the TweenService (GuiObjects have their own special function for this). In addition, TweenPosition has a parameter to prevent being overriden

Issues

Assuming this is a Server Script, make sure the Gui is parented to the player's PlayerGui or otherwise use a LocalScript and place the Gui into the StarterGui (in which case you'd have to reference the "part" directly, since otherwise, the Gui would not be visible to the player who touched the part.

Revised Local Script

local part = script.Parent
local menu = part.Parent:WaitForChild("ShopFRAME")
local debounce = false

part.Touched:Connect(function(hit)
	if hit and hit.Parent then
		local player = game:GetService("Players"):GetPlayerFromCharacter(hit.Parent)
		if player then
			local pgui = player:WaitForChild("PlayerGui")
			local clone = nil
			if not pgui:FindFirstChild("ShopFrame") then
				clone = menu:Clone()
				clone.Parent = pgui
			else
				clone = pgui:WaitForChild("ShopFrame")
			end

			if debounce == false then
				debounce = true
				clone:TweenPosition(menu.Position + UDim2.new(1.125, 0, 0, 0), Enum.EasingDirection.Out, Enum.EasingStyle.Linear, 0.2, false, nil)
			elseif debounce == true then
				debounce = false
				clone:TweenPosition(menu.Position + UDim2.new(-1.125, 0, 0, 0), Enum.EasingDirection.In, Enum.EasingStyle.Linear, 0.2, false, nil)
			end
		end
	end
end)