@Charles Granja it's actually the opposite. The VA underwriting guidelines are generally looser than Conventional and FHA.
And the lender you are talking to, who supposedly spoke to the VA, is dead wrong. Or they have overlays.
You can ABSOLUTELY use rental income from the house you are vacating without 2 years tax returns, because the VA guidelines allow you to offset the PITI with prospective rental income. You cannot use any surplus rental income over the PITI added to your qualifying income, but the amount of rental income up to the PITI can be used to wash it to $0.
The paid off house you can also use the rental income on the most recent tax return, as long as you have a 2 year history with other properties. Now, it will be prorated and may not show the full rental income, but it will be something.
The other thing to be aware of is that you will need a hefty amount of reserves. You will need 3 months PITI reserves for each of your properties. In addition to 6 months reserves on the subject property you are buying.
Now, if you are assuming a mortgage, then unfortunately you have to deal with that lender and their guidelines, which could be overlays to the actual VA guidelines. Either that, or they aren't trying hard enough to make it work.
If you are buying with a regular sale and not an assumption, be sure to work with someone who actually knows what you can and cannot do with VA lending, and is helping you to maximize your buying power.
TYFYS and best of luck!