Your relationship with your kids is really up to you. I hear from my girls that their dad hardly ever spends alone time with them. Yes, he married his affair partner so it isn't easy.
What I fail to understand, if you had your kids one day a week and every other weekend, wouldn't you spend every moment you could with them? The relationship with your kids need to be rebuilt between you and them, not you and your wife. You need to let them know how important they are to you. Your wife of course is also important but that relationship between her and them will need to take the backseat for now.
Please make the effort with just them, not because your ex is setting you up to fail but because the relationship with them is that important.
kat
Me-53(and learning!) S24, S21, D18, D17 Just keep swimming, Just keep swimming. Dory