1. Yes, you will want to do the partnership taxes before you do your personal taxes. The partnership return (Form 1065 and attachments) will need to be filed in order to generate Schedules K-1 for each of you, which puts the income you earned (or money you lost) from the partnership on to the personal return. Your personal return will not be complete without this information.
2. No, you don't need two different programs, but you do need to use a different one than where you have started. A partnership return can only be done in TurboTax Home and Business, which is only available on desktop. You will not have to pay for the online return if you have not completed, and you may transfer any information you've entered into the desktop program. Here is an FAQ on this: https://ttlc.intuit.com/replies/3302260
While you will have two separate returns to do, you will pay only one price. With desktop software, you may prepare and efile up to five returns for the same price.
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