How would I move a part relative to another part?

repeat wait() until game.Players.LocalPlayer
repeat wait() until game.Players.LocalPlayer.Character:IsDescendantOf(workspace)
----------------------------------------------------------------------------------------------------------------

--CONSTANTS;

local Player = game.Players:WaitForChild(game.Players.LocalPlayer.Name)

local Mouse = Player:GetMouse()
local MouseHeld = false 

local CurrentModel = nil 

--CLICK FUNCTIONS;

function CF_ONCLICK()
    if not MouseHeld and Mouse.Target then 
        MouseHeld = true 
        if Mouse.Target:IsA('BasePart') then 
            CF_FINDMODEL(Mouse.Target)
            repeat wait() until CurrentModel ~= nil 
            CF_DRAGMODEL(CurrentModel)
        end
    end
end

function CF_ONRELEASE()
    if Mouse.Held then 
        Mouse.Held = false 
        CurrentModel = nil 
    end
end

function CF_FINDMODEL(part)
    if part then 
        if part.Parent:IsA('Model') then -- assuming that 'part' is only in one model
            CurrentModel = part.Parent
        end
    end
end

function CF_DRAGMODEL(model)
    while MouseHeld do 
        if model:IsA('Model') then 
            model:MoveTo(Mouse.Hit.p)
        end
    wait()
    end
end

Mouse.Button1Down:connect(CF_ONCLICK)
Mouse.Button1Up:connect(CF_ONRELEASE)

Anyone else should use model.SetPrimaryPartCFrame. but apparently you do want to 'recreate' it

You just need to maintain all original offsets from the PrimaryPart. Best way to get offsets is toObjectSpace; originCF:toObjectSpace(targetCF). All math is behind the scenes.

With two parts:

local goal = CFrame.new() --change
part1.CFrame = goal * part0.CFrame:toObjectSpace(part1.CFrame)
part0.CFrame = goal --pseudo primary part

It's possible to move any number of parts by repeating the part1 line except with part2 etc. So, obviously put that in a part-loop, wrap with a function, and you have a generic model-mover!

--take array of parts, the primary part, and a goal cframe
local function SetPrimaryPartCFrame(parts,ppart,cf)
    local ppcf = ppart.CFrame
    for i=1,#parts do
        local v = parts[i]
        v.CFrame = cf * ppcf:toObjectSpace(v.CFrame)
    end
    ppart.CFrame=cf
end

hope you understand better