Is she still able to be blown around by stuff? I thought that stopped when she became untargetable. I never have any issues with sch and I don't even use dissipation or fey union at all.

SCH is a healer that requires a lot of practice to get the feel for the nuances and oddities. Once you get used to everything You can still go entire fights only using Adlo and aetherflow heals. I honestly usually have to use energy drain to use up a spare stack before the next use of aetherflow.

SCH is by no means bad. It just takes more practice and skill than WHM or AST.