Put some time in to tightening down those numbers. Get with a mortgage broker, or two, and see what you qualify for in terms of a new home loan. Ask about rate buy downs etc. Get some solid numbers on what a payment would be. If you keep your rental, it will affect your debt to income ratio. You may have no choice but to sell your current home. Also, look at what your rental income might be. How much of that income will the mortgage companies allow you to use as income on the loan application?
I would not piddle around with a rental. Even if you can rent it for $800 more then the payment, that does not mean you will be putting $800 a month in your pocket. If prices go up 10% on your hobby farm that is $50k. Your rental is gonna make you $5k. If you want the farm, you need to focus 100% of your finances on getting the farm. You can circle back and get investments later on if you want. (Like when the kids are older and can help paint.) You are making too much importance on your 3% rate.