Actually i dont see the point of suing the other woman. If a man wants to be faithful, he would be faithful at all cost. Anyone and anything can come and tempt but a strong tower will never be shaken. Personally, if i was the wife, i would sue the man himself for causing me misery and heartache and yada yada.
Nonetheless, adultery just like any other sins are punishable, and so is fornication according to God's Word. Even if it is not carried out legislatively, all those who know God's word would do well by not getting into it. But yes, again, to implement it is not a simple matter. There are many reasons and factors to consider. If we want to lump everything together and punish the offenders indiscrimately, then we would might as well have Syariah or Hudud Law, where adulterers are punished by being stoned to death or thieves have their limbs chopped off.
Having said that, if we were to do this then, Jesus wouldn't need to have done what He did on the cross. Do we live under the law or under His grace? Of course obedience to God's Words is no question here. But if we were to punish every sin on earth, i guess, there would be very few people living on earth here right now.