My advice is don't allow her to return home too easily. The OM is currently spending time at her place, and the excitement is wearing off. One way to end an affair it for that couple to start dealing with everyday life, which it sounds as if they are. So now prince charming doesn't look like much of a fairy tale, and she is getting a little homesick.
Btw, she can be homesick without desiring to rekindle an intimate relationship with you. The time to come to a full understanding and agreement upon the stipulations of her going back home is before you let in come back to the house. If you let her back and nothing has been settled, you will be right back in the mess again with OM #2.
Do NOT let her come home under the agreement that she'll sleep in a separate room! If she is not ready to share a room with you, then it's not you she is wanting to return to. You don't have to have sex right off the bat, but you do need to sleep in the same room. If she comes back under any other agreement, you M will fail. And, do not agree that there will be no sex. She is either coming back all the way......or she doesn't get to come back at all. Be very specific about it before she ever brings her suitcase through the door.
Dating...........is not near as important as her agreeing to be completely transparent accordingly to what you decide, when you want, and at your unsceduled time. She is the one who has to prove she can be trustworthy again. Therefore, she doesn't get to pick and choose what will be transparent and what will remain private. Nothing should be private between a M couple. Btw, this is not a tool you use to keep her under your thumb of control, it is a tool to help her be accountable......which in turn will help her beat the temptation to fall back into that behavior again. An example of transparency is you checking her phone, without previous warning or notice. She doesn't get time to delete messages, etc. She doesn't get a schedule to know exactly when you will check the texting, b/c you won't do it everyday, nor at the same time of day.
If your WW has an "attitude" about the conditions upon her returning.......do NOT let her back. It will get worse. She is the cheater, the betrayer.......and she needs to have a certain humility/remorse about those actions. She was willing to tear this family apart and mess up the kids' lives.......so don't take her back if she even hints of a disrespectful, cold, or bad attitude. Don't be hasty about going on romantic dates with her. The word "date" implies romance, and you don't need to rush for romance. If she can bounce from his bed to your bed with hardly getting her second breath........one of you are being played. You can plan on fun type of activity dates which have no romantic or intimate atmosphere, at least in the beginning of R.
Boundaries are the lines you have drawn around yourself that protects you. It shields you from being disrespected and harmed. If another person does something to deliberately bring embarrassment or pain to you.......then you need to do some type of action to protect yourself. In most cases, especially in relationships, there needs to be some type of consequence to the person who has not honored your boundary. It may be as little as you removing yourself from their presence......or as much as you removing yourself from the marriage. Boundaries are not ultimatums. They are not to be used as threats. They are no to be used to control others. They are used to protect you and what belongs to you.
If your WW is leaving hints she's thinking of returning home, play it cool and do not show that you are excited about the possibility. In fact, if she says any more about it, the first thing you need to tell her is if the OM is still around her place (even occasionally) then there is nothing to discuss. Do not play those games. She has to kick him out of her life, change her work shift or job so that she never bumps into or hears about him at work. She will have to go through affair withdrawals, before she's really ready to work on a marriage with you.
So, please don't get in a hurry........no matter if she has to pay extra rent or whatever, b/c this was her choice she made. She is experiencing a little reality and her fantasy isn't all she thought it would be. Don't let her make you feel sorry for her. It is not your job to rescue her. As a WW, she really needs to work to get to go back home again. Know what I mean? It is important for her, you, and the family/marriage.
I also advise you finding a very good MC to help guide you as you piece the M back together.........if she comes back.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!