No - your management hasn't the right to refuse you an interim reference letter! Upon Art. 330a Abs. 1 CO (Obligationenrecht) you have the right at any time to request a certificate about the nature and duration of your employment.
Furthermore the interim refence letter has to be - as the final one:
complete (naming all ...
So if I understand you correctly, you want one (interim) reference letter for your current position plus retroactively an interim reference letter for each of your two previous positions?
You can ask for an interim reference letter at any time (as Marc F. already wrote) but the letter is then issued based on the current situation (or from the beginning of your employment until now).
Of course, you can always ask, but I think that your employer could refuse to issue the retroactive letters.
Now it's too late but in general, I would always recommend request...