So, maybe it might help to re-frame the argument? Instead of fighting her to have only every other weekend, maybe the thing that makes sense is for dad to ask the court for time during the week. Document what happens with homework while the child is in her mother's care. Document anything that will help you make the case that it is in her best interests to spend some weeknights with dad. You obviously don't need to protect his weekend time as much because that's all she wants him to have anyway. Focus on what you want and why. Let her focus on what she wants and why. If it gets to court and she still doesn't want to have her daughter on weekends then you might end up with her every weekend and some week nights.
Nope has good insight. Focus on why DH should have some weekdays and not on why his ex should take weekends. (Except to show
Insight? Mother may want the best of both worlds. Weekends off to party or whatever, and all weekdays so she keeps majority time and get increased child support. (DH should be careful when the topic of CS comes up. He wants weekdays not to lower or avoid CS - avoid that stereotype - but because it's what his daughter needs.)
First, there is no CO yet, so all protests are just that, protests, not violations of any order.
Second, courts without exception see alternating weekends to have a proven track record. Of course there are exceptions such as for those on required rotating schedules such as police, fire, medical care, etc. Note that wanting every weekend off is not a typical demand made by a parent.
Third, courts generally want to see the parents involved with the child's life and that includes schoolwork especially if the other parent is not handling that well.
If school work is suffering - or even if it isn't - then a 2|2|5|5 schedule is a good one. My son had that from age 6 to 11 starting from when I became the Residential Parent. She had Mon|Tue and I had Wed|Thu (so I could ensure weekly work got done) and we alternated the 3 day weekends. It continues during the summer according to our new schedule where I have the weekdays during the school year. That recent change was because of the schoolwork, mother's behavior with the school and me and mother living outside the county.
It sound like your husband is asking or should be asking for a 2|2|5|5 equal-time schedule at a minimum. There are advantages to either early weekdays or later weekdays, ponder which would work best for you. I always preferred Wed|Thu, I was able to wrap up the week's homework at school and it gave me control heading into the weekend.
Is he also seeking to be
Residential Parent? In my area it's called "Residential Parent for School Purposes". That's what I did. I managed to get it because ex was looking bad heading into the trial and that was my #1 term to settle. I told her I'm RP or else we walk in and start the trial. Both lawyers insisted it didn't mean anything at all except for where the child attended school. Guess what? Mother has since moved twice, each time father away, I haven't moved at all. More importantly, after continued conflicts with mother in the next several weeks, mostly about exchanges at the end of the school day, the school gave me as RP one day to enroll our kindergartner in my school district. (My point, if I wasn't RP them her school would have been stuck with mother. However, I was the new RP and the school soon dropped her like a hot potato 5 weeks before the school year ended. Lawyers turned out to be so wrong in my case, RP was helpful (1) for son and (2) to give school reason to expose her behaviors.)
You can't force a parent to take the child if they don't want to, especially not a disordered parent. Number One is for father to get his weekday days. So just go ahead and start for a reasonably standard order such as the one mentioned here. If she insists on weekends off, that's up to her but DH should stand firm for getting at least two weekdays to monitor homework to ensure D does well in school. Judge may inform mother she doesn't have to take all her weekends but it has to be on the schedule? As I wrote, no judge will force a parent to take a child. Perhaps only give her 2 weekends per month, that means you've get the 5th weekend every two or three months. Or one weekend per month.
I feel DH should walk out with at least 50% time and Residential Parent. NO settlement should be for less. Yes, the judge could order less, hopefully not, but DH shouldn't agree/settle for less. For us, settlements are lousy half-measures that too often don't address the big issues. Mother is likely torn between looking like MOTY (Mother of the Year) and having her adult/party life.  :)H shouldn't trigger her unnecessarily but perhaps could use that to his advantage.