LAN isolation

Forgive me if this is the wrong place to post this, or if what I am
asking seems naive!

We have a situation where we have a customer who wants to use the
software available at www.logmein.com

They have a firewall which allows traffic in on port 443 (SSL port
logmein uses) - We cannot get access to this firewall, but as an extra
security measure can we isolate the PC that is being used for remote
access by using another firewall?

I am not a firewall expert, but the remote access PC only needs to run
one piece of software, which requires 2 ports to run (not sure which
ones, but the will not be standard ports). Can we put another firewall
in front of this machine and open port 443 (to let the logmein
software interact), and then only allow the PC to communicate with the
rest of the network with the 2 other ports? (The software will work
without logging onto the company network)

Is this possible? The logmein software seems secure, but say the
remote user PC was compromised and all the logmein passwords were
stolen, we would like to lock down the access PC so that anyone
logging into it does not get full access to the LAN (We definitely
have no access to there current router/firewall).

Any advice would be greatly appreciated.

Andy