Ideas
Similar issues: My understanding is that the doll needs to be in the world - not in inventory - in order to play with it or summon the Imaginary Friend. But, the Imaginary Friend dolls tend to disappear when placed in the world. Traveling seems cause them to reappear in the inventory.
Can't place a marble in the spot where the Imaginary Friend doll should be.
Traveled to a park. Doll is now in her inventory.
Did some testing. This isn't consistent. I played with four different children in different saves, different dolls and neighborhoods.
One had no issues with their doll. This was a test game living in a very simple quickly built Willow Creek house without a lot of other objects, lots of clear space. No idea if this is significant or just random. 🤷♀️
One sometimes seemed to lose their doll, but sometimes if I switched to an adult household member, I could see the doll and move it. When I switched back to the child it was visible and they could interact with it again. Sometimes only traveling would restore the doll. This was also a test game. House from The Gallery with lots of stuff and MOO. 🤷♀️
One always lost their doll on their home lot, but it reappeared in their inventory whenever they traveled. Keeping the doll in their inventory - when not interacting - seemed to work best. This was a copy of my regular game with mods/cc removed.
One - also a copy of my regular game with mods/cc removed - living in a r-rental had no problems. I don't use MOO with r-rentals (because it always seemed to cause issues) so ... 🤷♀️