This is my brothers situation not mine, but just wanted to ask for opinions.
My brother has a son who has just turned 4. He was never with his sons mum, it was a short relationship that ended before DN was born but they've co-parented the last 4 years and DN is a happy little boy with a great relationship with both parents.
Since DN was around 18 months they have done a fairly 50/50 split but I'd say in terms of 'responsibilities' my DB does more - he sorts most of his appointments, takes him to clubs and is generally very hands on and engaged. I can't speak for what his ex does as I really don't know her, but DB thinks he is the more 'primary' parent at this point. I suspect she would disagree.
Anyway, the issue is that they need to start looking at primary schools for next September and they can't agree on where his 'main' residence should be and therefore what schools to apply for. They both want it to be their address, local schools to them but they both live in different towns so drop offs and pick ups and therefore continuing 50/50 will be difficult for the parent who ends up not being the resident one. They both very much want to do it though. It'd not financially or logistically possible for either to move.
It's tricky because deep down and as a mother to my own kids I would never in a million years want their main home to be somewhere other than with me! As fabulous as my DH (and DB) is, I'm their mum and it would break me. But DB is adamant that this is just reverse sexism and if they went through court to decide she would 'win' just because she's a woman.
Would love to know what other mums think?