Respectfully request advice as newly divorced dad

Never speak bad or poorly of the ex, the kids mom.

Can't stress that one enough. The same goes for never putting your daughter in the middle of the situation with your ex. She doesn't deserve that, nor will she likely understand.

My parents split when I was 13 or 14, my old man frequently made remarks and statements about my mother that were none of my concern or business, nor were they likely based on anything besides anger and resentment. Even if there were truths to some of his ramblings, (he was usually drunk when he said things), no child needs to be involved in or informed of any behavior beyond what they see themselves.
Yes, believe me, kids do see and understand far more than adults realize, and they will typically internalize their thoughts and feelings, often leading to self-destructive behaviors. My dad was a very heavy drinker, and extremely abusive, both verbally and physically with my mother and with his 4 kids. Being the youngest I was least exposed, but nonetheless I knew what he was capable of, having seen and heard his tirades. I managed to stop the abuse part of the cycle completely because I was determined that I would never be like him, but I sure followed in his footsteps with the booze, at least until the last 5 years or so, I drink far less these days than I did for the previous 35 years.

You will be put in some very hard situations with your ex, but the best you can do for your daughter is put her best interests ahead of everything else. She may not always understand why you are doing some things, but the hope is that she will one day realize that your love for her was the driving factor in all of your decision making, and that you put her first everytime.

I am truly sorry that another family has to endure this process, it always leaves scars on all involved.