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It's hard to tell how your vehicle loan is impacting your potential new house loan without knowing your actual gross income. Did your loan officer go over all of your ratios for the loan (housing ratio and total debt ratio)? If she told you your loan amount would increase, I suspect that your total debt ratio is so large that it is affecting how much you can qualify for in a new home payment. Can you pay your car loan off early? It would help you in the long run.
As to going to Wells Fargo, or similar "big box bank" you may do better with a mortgage banker. First the loan officers are generally more experienced and will work with you to make sure you understand the process. Lately the large banks are replacing the experienced loan officers with just an inexpensive application takers - not a good way to get your first mortgage. Of course, YMMV.
A good loan officer is vital to the process. I'm in the home stretch of my first mortgage. I went with Wells Fargo due to the numerous folks here and on other boards that had used them for FHA. But I didn't go with my local branch. My realtor had experience with a lady a few hours away and gave me her number. I have done everything over email and fax and it's been a pretty painless process. She was quick to answer my email and return calls. She even went over the loan app and other docs line by line on a Saturday from her home. To say she's been wonderful would be an understatement. Wells Fargo gets it's share of hate but unless things fall apart at the very last minute my process has been very very pleasant.
If your DTI is close the truck payment could certainly make a difference. I want to say it's when you have nine months left they stop counting it against DTI but not 100% sure.
The number of remaining payments on your auto loan varies from lender to lender and the geographic area in which you live!
In my area of S Fl, it used to be less than 10 months worth of payments remaining on your vehicle and the loan was not counted. Then a couple of years ago it changed to less than 6 months and now they include the payment even if you have only one remaining payment!
I said geographic area above, but what is probably more accurate is whether your area is considered a "still declining market" like we are here in S Fl or if your market is stable. You have to ask the particular lender that is issuing the loan.