I'll add that you'd want to do some aggressive rebudgeting too and throw a few hundred extra each month at the van to knock it down if your goal is to rid yourself of the car payment. A high payment can knock into your DTI which would be a factor if there's not much extra to dole out now. DW and I were in the same position prior to our home. We aggressively added an extra $400 per month paying just over $1000/mo on it (tip: never sign a 72 month contract at 19.9% APR paying $606.41/mo like we did 
). The balance melted surprisingly quick. Once paid, we knew that we didn't have to worry about $600 hurting our DTI and that was $600 more in payments we could make on bigger home for our family of 6.
After paying off via the sell of the van, then please don't finance a new one. Then you'd be in the same boat and depending on your income, could impact mortgage approval, size of home, etc. I'd buy a beater that'll get you to where you want to go. Once you have your new house keys in hand, then you'll be in great shape to get a new car at a better rate if that's what you wanted.
Keep in mind also that you are unlikely to get anywhere near the values you are quoting if using the vehicles as a trade in on another used vehicle. Your negative equity is likely to be a lot higher than you think which will complicate your goal of reducing the payment on another vehicle.
If you want to find out what your situation is likely to be you could always go car browsing (as opposed to car shopping) and let them give you a trade in estimate. Just don't let them pull credit for a purchase and you will be OK.
Apologies to all the car salesperson for encouraging a customer to waste your time.
As a former auto sales professional 
I would never entertain an auto appraisal and trade estimates given would have 5k ranges. You can do you own research by going to an auto website and directing yourself through Black (not blue) Book Values/Trade In Values to see where your trade ranges.
FWIW I had a very similar situation so I'll share my story:
Last December I owned a pick up truck worth $2,500 and a pay off of 6K ($258/mo payment). I also owned a sedan worth $1,500 with a Pay off of 3K ($285/mo payment). I told my CU that I wanted to reduce my DTI by trading both vehicles in. It should be noted that the sedan needed about $2k in repairs.
I had to look for a pre owned vehicle that held its value but also had a large mark up to bury my inequity. (you can do the same with a new car just make sure the vehicle has a rebate or large mark up-MSRP vs invoice- price) than you can bury the inequity). I found a truck that had a 3.5K mark up. I negotiated that the dealer eat my inequity, and I paid off taxes and fees and remaining inequity (as my CU would only finance 100% of Blue Book) I had to put down 2.5K.
Outcome:
Before: After:
3 cars (2 of mine 1 DW) 2 Cars (1 mine 1 DW)
793 in Auto Payments 697 in auto payments
285 in Insurance 167 in Insurance
Total saving per month: $247 Per month $2964 per year!!!
Peach has the right idea. Sell the SUV and use the proceeds to reduce the principal on your van and the rest for savings.
Your high auto payments definitely impact your DTI and will reduce the amount you can finance for your new home. The best situation to be in for your new home purchase is no auto payment at all....this will maximize your available income for your new home purchase. Naturally, if you can not get rid of the payment prior to getting your new home financing, then putting yourself in the best position by having a lower van payment will help. Is it possible for you to sell other items around the house to put toward the van's payment to get it down so you can refi it with a CU for a decent interest rate? Sell anything not nailed down....