Hello and welcome.
How do you get there? Not like that. Certainly not like that. HE broke your trust, went behind your back for months and now you should miraculously be OK with it? That's just wrong and unreasonable. Before he starts asking of you to accept this new person in his life, he should work hard to regain your trust and try to make up for the damage he has caused.
Does he pressure you with the family? Saying that this won't be for the best of the children if you two were to separate? Children will notice if you are unhappy and they can tell that something isn't right and that you are suffering. Don't give them such a horrible example of putting up with things one shouldn't be able to tolerate just because some is making demands.
Don't ask others how you are suppose to feel. You should know how you are feeling and what the things are you want or don't want. Examine those and stand up for what you want and need and make it clear to him that he is in the place to do a lot of work for your marriage before giving being in another relationship even the slightest thought.
That would be what my take on your situation is. Wishing you luck to figure out your footing to stand on in this.
Facts: 30, female, bi, v-type relationship with Sward (husband, straight, mono) and Lin (boyfriend, straight, mono), poly-fi and co-primary.