@Mike Gammarino
If you can swing it without the down from your rental, then I’d leave the rental out of the purchase as well. But if that’s the only way you can make it happen, then there’s your answer. I used equity from a rental to buy my house...in hindsight I would’ve been better off leveraging that equity on other investments, but with hindsight it is always easy to beat yourself up!
Other thoughts:
Even if you don't do a cash-out refi, you could lower your DTI and monthly payment by just refinancing the principal on your home. You'll likely pay a little more in rates because it's not your primary residence, but it'll get you off the adjustable rate loan (which is only going to go up) and lock you in at historically low rates now. You'd want to look at what makes more sense based on your goals, pay off timelines, etc. but it's an option you should at least consider.
I’d 100% recommend doing both refi and purchase with the same lender-it’ll make communication and process flow so much easier! There are plenty of lenders that can write loans in multiple states. I strongly prefer mortgage brokers for a couple reasons: relationships, communication, access to multiple lending options vs. just bank lending vehicles, and while there are plenty of good bankers out there, I feel like the best brokers I know are just hungrier and more on your side (bankers work for/answer to the bank)...
Best of luck,
Mathew