The answer is yes you will have a problem with the appraisal. The situation that you are in is often referred to as upside down on your mortgage. You need to make sure that the information someone provided you is accurate before you sit back and say that your combined Loan to Value is less than the 1st and 2nd lien combined.
Appraisers work under state laws and regulations. In todays market appraisers will be very conservative as far as value because of the banks strict underwriting guidelines along with the fact that the appraisers tend to over secure themselves to avoid getting blacklisted with the lender. What that means is that they will never be able to do business with or for the lender ever again. The only thing you can do is turn to someone who will be able to deliver the best appraised value for your home to even complete the transaction and fund the loan, before you start shopping for rates, payments or fees. The bottom line is getting the deal done.
Before worrying that the value of your home is less than the loan amounts, you need to check the fixed period of your adjustable rate mortgage (ARM). You should also look at the index rate, margin, and caps of the loan if the loan is going to adjust. For example, if you have a 3/1 LIBOR ARM with a 2.25% margin and 5/2/5 caps you may be able to hold off on refinancing for a while. In this example the loan is tied to the 12 month LIBOR. When your loan adjusts, you will have another fixed period for one year before it adjusts again. The LIBOR is currently at 5.131%. If you add your margin of 2.25% to the LIBOR, your interest rate will be 7.381%. You will experience payment shock but not as brutal as those homeowners with subprime ARM. If you have a subprime ARM, then refinancing will be a very wise choice.
You have many challanges going against you. The main challange is the new value of your home, which, according to you, is lower then when you first purchased your home. The value of the property is very critical. You may not be able to obtain any loan with any lender if you are upside down. The appraisal with a lower value will be a problem in refinancing your home.