If I can give you my perspective without you jumping on me for it?
DD and I have moved "a lot" since ex and I split up. She was born in the marital home. By 14 months, we are in an apartment. Not far away, but still a different location. At 3, that apartment became outrageous for me to maintain financially and I downsized to a 1 bedroom 2 miles from dad (not that I was far before.. about 8 miles). We lived there a year. Then we relo'd to here. And now we are in an apartment here.
Now, throughout all the NY moves, I made sure certain things stayed the same.. daycare providers, whatever.
the move from exSO's to our own apartment here. Same thing. What she knew her kindergarten will be, is the same. Childcare/preschool. The same.
And she's EXTREMELY well adjusted with it. The school, when we relo'd to RI from NY, I had prepped them for a potentially rough transition, given dd's tendencies. After a few months, nearly every teacher in the school had cmoe up to me at some point and commented on how blown away by how well adjusted/unfazed by the change dd was.
It has happened again,with the transition to our own place and the removal of exSO from our lives. Because he was on the contact/approved to remove her list, the school was IMMEDIATELY informed that was no more. And once the office was notified EVERY teacher was notified. No such thing as privacy, lol. Anyway, so everyone KNOWS that we've moved (big change) and that exSO is no longer involved (BIGGGG change). And, again, they have marveled at how incredibly well she is doing. Yes, she's had her "moments" and she misses him, etc. it's not like it's had NO impact, but she's handling it incredibly well.
Why? Stability isn't necessarily in the "location", or the actual "house". Stability is in the knowledge/comfort of knowing regardless of WHERE you are, WHO will be there.
In the case of my daughter, she knows that regardless of the actual "house" we live in, I am the constant. part of that knowledge? Comes from there NOT being 50/50. And I don't think it would exist with 50/50 because her father has done as much transitioning etc, even if some of it is within ONE house (sleeping on couch, in the studio apartment, in his half-sister's room, then to his own apartment, then the girl sleeping upstairs, then back to downstairs, there's been no less than 3 changes just in the last year in one household as to who is sleeping where and with whom).
With me, having primary and having her 90% of the time, I'M the constant. And as long as I, as a person and a parent, am consistent with her? Our routines/etc are the same? Any other periphery changes are just that.. periphery.
Now that's NOT to say that she can't attach or isn't attached to anyone ELSE. NOT at all. She is NOT a clingy kid overall, although like most kids, she has her clingy moments/times. She's not terrified of things or afraid to join groups, play with friends, be around adults, be around other family. She has no problem forming attachments/bonds. She's very outgoing, highly personable, makes friends easily for the most part and is pretty well adjustment overall. So it's not like she's a "momma's girl" tied to my apron strings. In fact, the GAL in our case commented even BEFORE the move, how (despite the very limited contact with dad) comfortable she seemed with him, and me. She was very pleased that dd wasn't like "oh gosh momma don't leave me". She was like SEEYA! To this day? My daughter asks to go visit the GAL.
And I absolutely attribute a GREAT deal of it to how everything has been handled. And yes, I give myself a lot of credit. With dd's.. tendencies.. it could soooo NOT be the way it is. But it is. Because I've busted my butt to learn her, learn what works, learn how to handle her and NOT to feed those tendencies etc.
And no, that wouldn't have worked in a 50/50 situation. Absolutely not.