I have a somewhat similar situation to you gunnerzzzz. Not exactly, but due to false allegations, I was under supervised access for a while and one of those days per week was while the children were at daycare. I felt like that established the attitude of the daycare centre towards me so that even when the allegations were essentially dismissed and the risk was determined to be low, I got the supervision removed and equal shared parental responsibility was upheld but I still felt like for some time, the daycare centre were not treating me like an equal parent. Because my orders only gave me specific hours on specific days, I was totally excluded from communications and special events (fathers day dinner, etc). I didn't even know they were having a fathers day event until the day of it, and of course as it was in the evening, it fell under time that my ex had so unless I could get to her to consent to the children attending with me with just hours notice (she would never agree to anything she didn't have to), I couldn't do it. They also would not give me the door code to the building, despite the fact that every other parent was given it, so I was forced to wait for staff to open it for me. I was being treated like a second class parent.
The daycare centre also said they were responsible for enforcing court orders, despite the fact that my understanding is that it is not their responsibility. They should obviously be AWARE of court orders, and alert the other parent if there is a breach of them, but should not interfere with parental contact unless they identify a genuine safety issue.
Cooper Grace Ward Senior Associate Craig Turvey discusses whether schools have an obligation to enforce parenting orders.
legalwiseseminars.com.au
The above article seems to agree with me on that point, although it appears there is still confusion out there because some other articles/guidelines say otherwise. A recent discussion with a family report writer revealed they also thought it was the daycare's responsibility to enforce court orders... Confusion reigns.
Ultimately though, over time, the daycare has realised that I have no intention of breaching the orders and simply want to be an involved parent and I'm hoping things will be better in 2020. I can only reiterate the advice you've been given and what you've realised yourself... Be firm but don't appear aggressive or confrontational if possible, because that's only likely to make them worry you'll storm in and abduct your child out of nowhere - a nightmare scenario for any daycare centre.
Parents shouldn't have to walk on egg shells to have the contact with their children that they deserve and the court has already ordered, but there you go. It's all part of a biased and unfair system that we have to navigate. Not to make everything genderised, but we live in a world where mums are assumed to be better parents, where dads are all potentially domestic violence perpetrators, and most daycare staff are female. It's not surprising that they will see things through their own tinted lens.