Does this gift come with the expectation that you will provide her a home indefinitely?

But a 1031 exchange where you replace that real estate with other investment real estate (of any type or passive or active) allows you to indefinitely defer all tax on gain and recapture of depreciation.In your case with the right replacement you could turn this sale into a completely tax deferred sale that also reduces your net loan liabilities personally, provides income for you, and adds depreciable basis for you to write off. 

I’m considering having a property  management company run it for a while until I learn the ropes or indefinitely.

So that in a couple of years they can move in and convert it to their primary residence and continue to defer indefinitely. 

The cash and the note must somehow be used toward the purchase of your replacement property if you want to indefinitely defer all of your taxes.  

We plan to stay a year to renovate, then move on to the next house and keep the first house for a rental indefinitely.

You can deduct your mortgage interest, defer your capital gains indefinitely or even qualify for an exemption on capital gains altogether.

This will allow you to defer the taxes indefinitely until you sell and take the gain for another purpose other than real estate. 

You must have some serious cash to invest if you can indefinitely continue making large purchases that don't really cash flow.

With the pandemic, I had some life events that necessitated moving out of state indefinitely, and rather than sell, I decided to rent it out to at least keep the mortgage paid.