I think that the courts have their ways of dealing with frivolous lawsuits. People that lie to the court are found out - most of the time, not all of the time - and that's one situation you really don't want to find yourself in.
Really? I was under the impression -- at least in the US at the local/state level -- that perjury was not a highly prosecuted crime. In most cases, it was just a charge that was brandied about to force a confession or something similar.
It might be different if you're the star witness in a big case, or you're the one that's actually bringing the charges...
In most domestic disputes, things really end up in a 'he said/she said' situation where there aren't many facts to back things up. Which is why the courts hate dealing with this. You end up having to just listen to both sides and try and make a decision about which person is more believable...
Lying under oath is generally not a good idea.