As I mentioned, you "break into" a protected network. And the goal of the firewalls is to hinder access from outside to inside. And as you stated, you want to "break into" your own system. If this is true, you have the means to:
A) either change firewall settings, to let MineOne (but only that machine) get trough it, and reach DestOne directly,
B) or to install a proxy (as Dave explained). Proxying is dangerous! Why? Because it is blind if you don't implement access control, letting somebody use the proxy, you open your whole protected area. So be careful to use proper access control.
C) or even better, to install a monitoring system on SourceOne to monitor DestOne, and you could expose the monitor or service via the firewall
D) remotely execute code on SourceOne from MineOne. Have you tried
psexec[
^]? What you can do in psexec, you can do also in
c#[
^]. So if you have a user with proper rights on SourceOne, you can remotely execute something like
tcping[
^] for example.
There is an other scenario I can imagine: SourceOne is a gateway between two physically separated networks. If this is the case, option A is not usable.
Just a note telnet, is dangerous, since it is not encrypted. I you can, switch to ssh.