I have been using Time Machine to make full, separate backups of my Macbook Pro on a Time Capsule and on a 500GB external hard drive. Time Machine makes alternate backups and it has worked well.
I would now like to use a new 250Gb SSD external drive to make a bare-bones backup (e.g. excluding music, pictures and video). In Time Machine preferences I have excluded the folders and got the backup size to under 250Gb. That is fine (the SDD is very fast) but my problem is that these folders are now also excluded from the Time Capsule backup. There does not seem a way to have different exclusions from different backup drives. Or have I missed something?
No, your conclusion is correct. Instead of using Time Machine for the SSD, try using a cloning program. That will allow you to reset Time Machine to backup everything.
Clone - Carbon Copy Cloner (Often recommended as it has more features than some others)