I'm glad Mrs Dools has spoken with you , she is a person with a lot of wisdom. As she pointed out you mum may well have been emotional about the funeral to start with, and comparing yourself with others simply does not work. In a world of TV, magazines, catalogues and all you are always going to find some that are slimmer, blonder, and so on.
It gets to be a habit and so you compare yourself with your sister, which is not fair to either of you (you have good points too you know).
Saying 'see ya' as a parting goodby is perfectly acceptable, I can't see any reason why your mum would be unhappy with that. It does mean 'goodby' in some circumstance, and that was one of them.
You asked why you felt like a disappointment to your family. The short answer is because they are making you feel that way. Parents have a huge influence, much more in fact than they might realize, and criticizing too much is harmful. Sure some criticism is OK, but there has to be a balance. Letting a person know what their strengths are, and giving praise are even more important.
If you sister finds putting your makeup on is more successful than you doing it, well that's not surprising, doing it for yourself is much harder.
Basically your mum needs to know she is doing harm, even with the best of intentions and love. Can you talk to her about this? Alternatively is there anyone else in your family you can talk to?