As for finding the centers of the circles, I don't know a recursive formula, however if you need to draw a picture of the Appolonian gasket, you need to be able to compute the centers of the circles, so clearly many people have solved this problem. I would suggest looking again at Indra's Pearls to see if they explain how to compute the circles, or look at the source code of McMullen's program lim which generates postcript to draw limit sets of Kleinian groups.

$
e =  2(b+c+d) - a \\
f =  2(c+d+a) - b \\
g =  2(d+a+b) - c \\
h =  2(a+b+c) - d \\
$