B.W.
Honestly, I found steam cleaners to not be that good. I have done everything from renting them then having a service doing it. I haven't been impressed. I do have my own Bissel but it doesn't do so good. I actually hire these guys named ChemDry that do a fantastic job and are well worth the money. However, your carpet sounds lke it needs more restoration than just cleaning. Look into a service. They have huge scrubbers and can do the job in a fraction of time and get the carpet much cleaner. I know it costs some money but time is money. If you spent hours doing it yourself- that is time missed out with the kids. That's how I look at it.