Your line in this hand?

[Snarf]

3 handed with slight chip lead. I have say 6500 or so. Button has 3500ish and BB has 5000ish. Blinds are 200 400. I pick up pocket 4s in the small blind. Button raises to 900. I re-raised to 2000. My image is a tough LAG who has been raising QUITE frequently and could have a WIDE range of hands. So obviously when the button goes all-in and I figure her for two overcards, its an insta-call with odds. If I lose, I'm fairly short-stacked with only 5 BB. I figure I could get my money in again with a decent race which I could be back in the hunt if I won. I lost both that race and my next race (my KJ to AQ). So I take 3rd.

So my question is this:
Whats your line there w/44 knowing its a coin flip?
Dump it - not risking getting shortstacked over a coinflip?
Call - see what comes out and play your reads from there?
Push and accept the coinflip if the button calls/goes all-in?

Its sort of a third or first type of race...but I probably could've pacified my way/chopped out small pots down to heads up and played for the win from there.

Pay out was $10 $25 $35

Whats your line? What do you think?

Three handed, do you take a coin-flip for 3rd/1st? Or keep it post-flop and chop it out to heads up?