remove pmi and get heloc on primary residence

[Patrick Mortenson]

newbie question about how to remove pmi and get heloc.

we have owned our home for about 4 years now. this is our only house, mortgage is held by freddy mac, servicing company is qrl. the county recently reappraised our house for the next tax year and thinks the value has gone up enough to give me over 20% equity. i called the loan servicing company to ask about dropping pmi. they say they wont go by the county estimate. they want me to pay them to send an appraiser out.

im also considering looking into getting a heloc just to have open as an emergency fund.. which would need another appraisal. 

im wondering if there is a way to somehow do both of these things and only pay for one appraisal. at over 500$ that would be a lot of money for me to pay twice.

also, would there be some kind of conflict there? trying to remove pmi while at the same time opening up a heloc?