To a large extent it is normal for kids that age to have separation anxiety when you leave them at daycare. Both my kids use to cry when I left them at nursery and both would jump on my when I walked through the door at night - in fact, coming home was my favorite time of the day for just that very reason. But you are right, kids know when things are not right at home, no matter how hard we try and maintain civility and it is our job to try and minimize that change and make sure they feel loved and safe. Give them love and try and maintain a routine which includes taking them to childcare, giving them a hug, telling them you love them and will be back for them, and then leaving.
Your W isn't trying to tell you how to be a parent. She just doesn't want to leave them. So she fusses. She wants to make sure she is still needed. This isn't about you or about you and her, it is about her role as a mother. Do you know those scenes in movies when the parents take their kids to college for the first time and the mom starts to fuss and ask questions like "Do you have X?" or "Did you bring Y?". It's not about not trusting you with the kids. It's about not wanting to let them go.
I know it hurts because you see her wanting to be a mum when she was (is) such a terrible wife and all you can think about is the damage she's done but honestly, this is not about you. Show her you are not only a good dad, but also a good man. When she offers advice, thank her and say "It's ok, I really do have this".
By the way, I like the IHCLACs take on why some parents suddenly double up on being a parent after a separation. I had never really thought of it like that. I saw my H taking his love away from me and at the same time, doubling up on his love for the children and even our dog. I wasn't jealous exactly - it's our kids and our dog, but it still hurt. The love doesn't just up and leave. It just needed somewhere to go.
