A.B.
I am going to be in your position in 2 months. I already cave every time my daughter requests "up".... so, now you have me thinking. if it will get worse when the new baby comes, I need to set some boundaries myself!
Anyway, I really liked the advice you got about explaining that if she doesn't start to learn to deal with dissapointment and "no" now, she will actually be more unhappy later when she can't get what she wants because she won't know how to deal with it.
Can you give him a concrete dinner offer? Tell him to offer her chicken or meatballs.... for example. If he really wants to give her an offer, that sets some boundaries while still allowing her to feel in power of her choices.
I realize you only gave a sampling of specific behavior to us. But rather than abstractly telling him to set more boundaries, tell him exactly what needs to happen. She is being put to bed at 8:00 one way or another. end of story. I mean, kids can't even tell time yet, so 8:00 and 9:00 is the same to them. Let him know that it won't upset her to stick to her bed time because she doesn't even know the difference.
As far as the treats and cookies. That is just not healthy. He must want what is best for her. Giving a toddler sugar is not healthy. Soon enough he won't be in control of how much she has and he doesn't want to set her up for an out-of-control sweet tooth. She will be much more unhappy later in life if she has to battle weight issues.
Anyway, maybe the compromise can be that you two discuss what is actually harmful to her and what isn't. Maybe you can cave a little on the picking up and whatever else that may seem like spoiling, but doesn't harm her. And he can stick to some of the rules that affect her health and safetly. Have a conversation about which rules fit each category. If you decide that there is no harm in some of the things he gives in on, you can "spoil" her a little in the day with those things and not be such a bad cop. And you can comfort him into realizing that she is still happy and getting her needs met, so he doesn't need to go overboard with the unhealthy things.