There is no restriction saying you can't get an FHA loan with also having a VA loan as well. You just can't generally have 2 VA loans or 2 FHA loans outstanding at the same time.
However, you would need to qualify for the new loan AND the existing loan payments, along with all your other debts. And unless you have 25% or more equity in the VA home and are moving at least 100 miles away, rental income from the VA home cannot be used/considered when qualifying for the new home.
If you can qualify for another home considering those factors, then nothing keeping you from pursuing a single family home for yourselves using the FHA purchase program. Hope this helps! Let me know if you could use assistance getting pre-approved!