I don't think ADU's have and restrictions on refinancing, and with interest rates at all time lows, it's likely that you could really lower your monthly payment. You're definitely smart to research your options. Good luck!
Mainly, the cost to refinance and how long it would take for the savings to offset the cost.
You need to speak with a lender that can show you your options in writing and explain to you what the benefits and costs are.
Here is some more information on refinancing: http://www.elliottoliva.com/WhentoRefinance
Here is some more information on Mortgage Insurance: http://www.elliottoliva.com/FHAInsurancevsPMI
For more details or questions please feel free to contact me at your convenience. Thank you.
You should call your current lender and/or reference your mortgage paperwork to determine if this can be done. Just because you have 20% equity does not mean you can remove the PMI. Some mortgages have certain time frames before you can refinance or get rid of your PMI. If you need help determining this, you can call the loan officer that helped you with your mortgage (if you liked him/her) or you can contact someone new and I'm sure they'd help you to find the answer.