Hi @Matthew Hanbury, I'm sorry to hear that you're in this position. I'm not a lawyer, you should definitely consult one before taking action, but here are my thoughts.
I think this decision should have been sorted out in your divorce decree (who continues to own the property, who remains on the mortgage, etc.). Keep in mind that being on the mortgage and property ownership are separate topics. Re-read your divorce decree and your talk to your attorney before planning anything else.
Keep in mind that if you need to refinance, you'll need to requalify for the mortgage. Does your DTI support $1750/mo?
Finally, I suspect that you've been through a lot in all of this. I applaud your desire to start a small rental property business, but you don't need to do everything at once (finishing school, raising kids, starting your business, etc.). I'd suggest taking things one step at a time, setting yourself up for success in the long run.
Feel free to DM me if you'd like to chat about anything privately.