My advice is take things step by step. Your debt to income ratio to purchase a new home is your primary issue. VA loan won't help you because of your debt to income ratio. However, if you rent your current home sometimes you can count towards your debt to income ratio and it cancels out your mortgage. Then maybe you can use the VA loan that is no money down, no pmi - good deal. Rate is a little higher, usually, but rates are so low anyway, may still work.
Ask around to some lenders. Sometimes if you have a section 8 housing voucher holder rent your property, since the income is guaranteed, some lenders will count towards dti without rental history.
If you can do this and want to do this, then I would suggest you talk to some professionals to help you with both the rental and purchase. Some of my clients have one partner take the lead if there are scheduling conflicts. Good luck.
Your best formula for financial success will be to sell your current home prior to going to contract on a new one. It's best to not overlook the lesson learned by many that ignored this basic idea before ushering in the housing melt down that we are still trying to put behind us.
Being able to prioritize and take things sequencially should help you find the peace of mind you are so much in need of.