Wanted: a personal proxy program (for desktop and laptop) that is able
to rotate private proxy servers (that require login-information). The
program needs to be stable and perform when using multithreading of up
to 100 threads. I am willing to pay a maximum of $ 100 to use this
program. Where can I find such a program?

While it might not be exactly what you're talking about, and while
it's actually meant to act as a proxy filter so that users can filter
out (or in for that matter) content from http packets, Proxomitron
(http://www.proxomitron.info) may be what you're looking for. It has a
proxy rotation option that allows you to specify whether you want
linear rotation (just run through the list) or random rotation. You
can also specify however many connections you want before the rotation
is made.