I like to work on the assumption that the OP is being honest and upfront - it's an anonomous forum after all - but your consistent vagueness makes me 100% certain we're not getting the whole story.
50:50 care? Okay, so then why not organise milestones during his 50% time? Birthday? DC can do something with mum and something with Dad. If care is 50:50 and court ordered, dates like birthdays, christmas, easter, mothers/father's day can and should also be in the court order and evenly split.
"Dad pays for everything" What does this mean? But, again, context is everything. Is dad paying maintenance? Or paying for clothes, presents, tech, uniform, hobbies? Is mum really not paying at all?
Why is ex's feelings so anti dad? Most people aren't wild about their ex but unless things were very bad, there's usually an ability to be in the same place, at the same time, when necessary.
This is alls ounding vey much like, "my ex took me to the cleaners" without a shred of actual proof and the new woman laps it up.