Valentine was a priest that was imprisoned for giving the rights of ordinary folk to love each other, he was jailed in order to send the men away to war away from their loved ones. In prison there was a blind girl that was called the "gaolers daughter". Look it up on the web its there.
The way i see this - in the first place what was her reason for leaving you in any event that she gave to you.
Secondly as you say you suspect her of having an affair and she won't admit to it. (I can imagine how painful it must be for you, excuse me for saying so). However if you was to prove that she is having an affair with this person, without being maliciously untruthful in a divorce proceeding. Then your rights within the divorce would have stronger values than hers. It seems a pity that you give up so easily when you have been together for such a long time and you have also to remember about the well being and care of your children, surely that gives you the determination to fight for your rights predominantly within the divorce. All the best.
My job was to work in Civil Litigation inclusive of matrimonial and the care and custody of any children within the family.
It is very difficult to give a straight answer to your question not knowing the facts. There must be some sort of dispute on agreeing the final decree to postpone the settlement. Has your own solicitor thrown any light on what the problem is?