Is it still romantic if there’s nothing physical more than a hug?
Yes, in an emotional affair like this, there is a spark, romantic closeness, and reliance. Is this a dealbreaker for you?
Of course, except for the embracing, you have no idea what the physical parameters of their relationship are. They’re attracted and closely bonded, feel entitled to share elements of a boyfriend/girlfriend dynamic, and are out together frequently, so there’s always the chance of physical involvement.
Knowing they’ve been on outings together with the children is troubling.
Well done for assertIng your boundaries and self-respect and taking space, @Fassbender2020. As you signed up for monogamy, it’s entirely inappropriate for him to be in this intimate bubble with this OW he fancies.
He’s got me and if he doesn’t want me then he should go.
He’s not going to say he doesn’t want you. He’s greedy. He clearly wants to maintain both relationships, as together they meet his wants/needs. He will attempt to manipulate you so he can keep the status quo at home, with an affair in plain sight. Don’t allow him to bamboozle you with denial, feigned cluelessness, or deflective accusations (insecurity, unreasonableness, overreacting, jealousy, etc.).
Tell him what you’ll no longer tolerate. Tell him he can keep his girlfriend, but not while married to you, and mean it. Personally, I’d end the marriage and leave them to it.