as an appraiser, nope
as a consumer. maybe. if i want that shiny new car and dealer A will only sell it for $5,000 but dealer B will sell it to me for $4,700 i am going to go with dealer B. there is always a chance that the second appraisal will come in higher, but then you have to ask yourself if you are willing to spend (borrow) more money and potentially be underwater from the start. it has happened in the past but asking for a 10% increase is a lofty goal.
if i were in your shoes the first thing i would do would be to go to
www.ASC.gov and look for a local appraiser. call them, talk with them and see how you feel about them after that. i would personally want someone with a minimum of 10 years experience in that specific market, and someone who has experience with higher priced housing. spend a few hundred dollars and have them review your appraisal. that way you can have a second opinion from another disinterested and unbiased party about the value of your house and if you are way off or the sellers are. $400-500 is a drop in the bucket compared to a $600,000 purchase. my dad will drive 10 miles out of his way to save $0.20 on a gallon of gas