I agree with what @Billy Daniel said. If you can refinance your current mortgage to conventional loan and still cash flow renting it out with the new payment I would do that. If not, you are probably best to sell and use the equity elsewhere. Either way, you should definitely get another VA loan when you move and put as little down as possible and not have the PMI still. You have the equity from your current house to either invest or use to capture some forced appreciation on your new house.
I think you should be ok from a job perspective. You have to show a bank recent paystubs and 2 years W2s. The furlough likely won’t be reflected in that. IF an issue does arise you should be able to get a letter of employment from your employer to provide the supporting documents you need. A lender would be able to give you more information (you don’t have to reveal your husband was furloughed, just give them the documentation they ask for when getting preapproved and they will ask whatever questions they have from there).
And definitely go for a house hack!