So good to hear from you - my thoughts often turn to you and your situation and my heart aches. I'm very glad your counselor spoke to your husband of the harm in having your children meet this other woman: what a piece of work she is. Not only is she damaging her own kids by pushing them to meet your husband, but she would intentionally do harm to them in wanting to meet them so soon.
But I sit back and think (this is my opinion only) that a part of the difficulties you and your husband experienced in your marriage was due to his frequent and extended absence from home. Will this change in the future if and when he decides to go ahead with this OW? I doubt it. He will continue to travel and this OW will then experience what you have to put-up with over the years - being a single parent: and I highly doubt she will enjoy it as she has been use to his undivided attention and presence.
Not only will she be looking after her own 3 children (I am surmising the husband will not have full-time custody [though for their well being he should]) but may also be looking after your three children at the same time. In future you children could be visiting with them, your WH goes away on business, and she is now watching after 6 children. The bloom is certainly off the rose.
She will very likely blow-up at him for 'leaving' her to fend for herself, and their 'now perfect relationship', will be come as mundane and everyday as the rest of us: mortgage payments; bills; day-to-day living. This scenario was not what they expected when they began their illicit relationship one year ago.
I hope for you and your children that the forcing of your WH husband from your home causes him to have a reality check and realize what he is losing-out-on. I'm also very certain your daughters will not look on him quite so kindly when they realize that he has abandoned not only you, but them. He will face hostility from them and be forced to realize his 'pipe dream' of a perfect ending is nothing more than a bunch of hooey.
At that point you will be in a better position to decide the outcome of this situation. It seems right now, that he is making all the decisions. It is time he has a very rude wake-up call.
I continue to wish you all the best and keep you in my prayers. Continue to enjoy the time you spend with your male friend and work on making yourself happy.