So to be clear, I'm looking after a dog for a charity with the aim being to sort out some behavioural problems and eventually get it a permanent home. In the UK, we'd just say 'we're fostering' and everyone would know what I meant. It's the same term as for kids.
When I try to explain this to anyone in Spain or Latam, they get confused – reverso.net has the term 'acoger' as here
but I think that's only in Spain and even then not very much. In Latam it's sometimes called 'una casa de tránsito' but how do I use that? Do I say something like 'tengo una casa de tránsito'?