(have name changed for this)
I am the woman in an equivalent marriage. We have had no true intimacy for many years; children, money, time...several other reasons too which I wont go into here.
As with yourself, on occasions the grass has been greener, and there's been a lovely man holding the gate open for me, but I haven't (as yet) explored further. You have to look past the thrill of the new, the romance and the sense of being desired - and being seen as desirable - and consider long-term where such a choice might take you. Do you still love her enough to truly address what's happened between the two of you, do you believe it can be resolved? Are you prepared to accept the impact a split would mean to yourself, your DC's , your income, and of course, your DW. Or has the dissent gone too deep and too far?
For us, we've spent hours and hours and time away from the children to address this. He is only learning to understand that, for me at least, sex isn't a perfunctory kiss and get on with it. Intimacy starts at the beginning of the day, through noticing and commenting on how you feel about that other person (how they look, what they did), finding some way to demonstrate that he finds me attractive and desirable at any point in the day. A touch, a caress, a compliment - these may seem small but (imo) for a woman sex starts in her head way before she even considers the physical aspects.
And finding time is so very hard with children about. The demand on many womans' emotional time is huge, so much so that there sometimes seems litttle space for anyone or anything else. The exhaustion, both both of you, can seem overwhelming. Perhaps consider reinstating a weekend away without the DC's every few months, and if that isnt possible just an evening away from the house for the two of you.
Talk with her. Alone, no counsellor. We all deserve happiness and fulfillment in life, people - and their relationships - do change. Only you can decide if yours is salvagable.