The counselor is right only in that your husband will never end the affair and be committed to you again until HE WANTS those things.
He needs a dose of reality. Here are your next steps and no, you won't like it but it's the only way to burst his OW fantasy bubble.
1. He must leave your home. He must move into an apartment or rooming house - not live with a male friend or guest room of a family member where he pretends to stay while living with OW secretly. Or a place where his parents watch your kids all day and he does little of hit himself. He says it's too costly and expensive to live separately and pay double utility payments, water, , internet service etc? Then tell him what the hell does he think would happen in a divorce? Does he think OW will support him entirely while his money goes to child support etc? Inflict reality on him through this.
2. He must "babysit" his own kids in his apartment and not do so at your house while you are there or out of the house, but will have to take care of them HIMSELF, 24/7, on his own every other weekend or whatever schedule you choose, and no assistance from you. He can't pretend to be head of household in your house - having two wives, one who raises his kids and one he screws, or screws both. He has to be treated to the reality that he will experience consequences, that his life will change in a divorce. Not being in your home, at all, except to pick up kids at the door for his visitation, would be how the divorce would be. So he should now, as long as with OW, have to entertain his kids, bathe them, chase after them, feed them, and do it 24/7 on his own in that apartment or rooming house where he has the kids for an entire weekend. If he watches kids in your house, he doesn't have reality because he gets to play dad and groceries are there, you're there to take up some of the slack and he can go party that night or do what He wants to do. He needs them a full three days, and you'll need the break anyhow for hair, nails, any kind of restorative help if only lunches with a best friend and movies that you want to watch without chasing kids all day.
3. Tell tell him if he moves in with OW, or has her looking after the kids because he gets bored doing it, then you'll file on grounds of adultery rather than on grounds of one-year separation or unreconcilable differences. Tell him that you do not wish to raise your children with values that it's OK to fuck around while married and to have one's latest fucks watch the children. That your values are that a parent does the parenting, not a girlfriend, and for all you know she's a coke-snorting party girl who isn't suitable to be around your kids, or would lose it around kids or could be abusive. That UNTIL HE IS MARRIED, he can't have his fuck partners in house with kids and sleeping with her in front of them.
4. If you have legal separation in your state, then consider this, so that he won't get loans off credit cards or elsewhere, using your name as credit, since as long as you are married and not legally separated, he can legally get cash to buy his OW diamonds, vacations or whatever, and you would likely be stuck paying for half of it in the end. Or get advice from a lawyer of how to prevent this from happening. If he divorces you, then judge could award you 50 percent of your husband's debt to pay off. Even if judge doesn't, and your husband refuses to pay off debt, the credit companies and banks will come after you and hound you to death no matter what judge ruled.
5. If you know you can't afford the home with your income and child support, that it takes both your incomes for all utilities etc.... then you need to begin cleaning and making repairs to think ahead in case it must be put on the market. If you don't divorce, you'll have a less-cluttered home in better repair to ease stress during reconciliation, which is hell even under the best of circumstances. If you do divorce, then you won't be sorting old baby clothes and toys and photos and crying at the same time you're dealing with decrees and lawyers.
[This message edited by Heavy Sigh at 12:02 PM, June 8th (Saturday)]