Can you link to an example on the map? Is it rendered at all?
If you have a area tagged with building=yes and amenity=pub then it renders fine as a building with a pub icon etc. Though the garden isn’t a building - maybe have an area with building=yes next to an area with leisure=garden?
Also, I don’t think the car park should be tagged as amenity=pub, as its not actually part of the pub. Just as a supermarket car park is not part of the shop. Just draw it as a separate area with amenity=parking, plus name=pub car park or whatever.