You obviously are considering the option of saving your marriage because you are here. Kudos to you. So let's take that and work with it a bit here before we go off issuing an ultimatum.
If you haven't already, pick up Divorce Remedy, Divorce Busting and Men are from Mars/Women are from Venus. I strongly suggest the later book also because it explains the differences between men and women, their needs, their thoughts, their interpretations.
Women have different needs from men, obviously but their reasons for having an A tend to be more emotionally based. Spend some time on the Newcomers thread about recent success stories. Look at the ones written by the men of DB. Most you will find won their wives back through friendship.
Also spend some time reading Franks, Tims and TMUs current threads on here. They are starting to just realize their roles in the demise of their marriages. Each one of them have received excellent advice from other members on here.
You are already separated, currently your W does not find your M attractive or she would not have left the house. Issuing an ultimatum is something that is done when you know that you can live with the final decision. Its a form of control to the WAS. It often pushes them further away instead of attracting them back towards you, which I am gathering is what you want since you are here. But to each their own. We often tend to react to things quickly, living in a FedEx world where we demand immediate fixes to things. Instant gratification. But honey, it took sometime for your marriage to fall apart to the point where your W had an A. Trust me, this is not an overnight fix. It will take a great deal of work on your part to dig deep into your inner being to find your way and find your part in all this. Because at this time, you have no control over what she is doing/feeling and if you dwell on that you will go crazy. You only have control over yourself.
I agree the begging, pleading etc...not attractive, certainly not to your W either, since again at this time she's not looking towards you. This is why you will find that despite the rollercoaster ride you are on, you can control the ups and downs. You go out and GAL, do the 180s, work on yourself. Find yourself again. You prepare yourself for either the return of your W to start over again (the old M is dead) or you are prepared for a new life without your life without continuing the vicious circle. There are issues that you have and your wife has. You have the chance to work on yours and for now your wife has chosen to run from hers.
3mos is nothing in the scheme of things. I know it feels like the end of the world. As run typically from 6mos to 2yrs. Why because it takes at least 6mos before you get to konw someone...and then the real world starts setting in. Initially the A is wonderful, they see the op is their rescuer and slowly but surely the op starts showing their true colors...but if you are consistent in your efforts you can show your W the way back to your heart and home. It's work...hard work. Yes you can always take the easy way out, but that's not why you found DB is it?