Hi, I think you are being far too hard on yourself and because you are down and anxious and your little girl is picking up on that.
I have an 8 yr old who is sometimes anxious/reluctant to go to extra-curricular activities.
As pseudonym says, it depends on the individual child, and only you can judge whether this is a really deep seated fear and extreme anxiety or the ordinary/normal apprehension at having to do something she is behind in/not enjoying atm.
Once you have decided that, you can act accordingly.
However, if it's the latter, I personally would d suggest that you try and encourage her to go (but you must be consistent - don't say she doesn't have to go - and then change your mind and persuade her ). Make a decision and stick with it (I'm not being snippy saying this btw - I've done exactly the same thing as you many times, and my dd has exploited my indecision ruthlessly
!!) You and your dh need to take a consistent approach too.
The reason I say this is because I think it's a good lesson to teach dc the appropriate way to react to things- and if it's really not a scary thing - then it's good to go through with it (even though it might be a bit unpleasant/boring) and experience that it actually it wasn't so bad after all. And that way they learn a bit of resilience and don't run away from their fears.
I think if something really isn't scary or bad, then we as adults, owe it to our children to explain that and follow through accordingly.
As adults, we often don't want to go out and do something that's arranged (even sometimes when we have been looking forward to it), but nine times out of ten we end up enjoying it. I think dc go through exactly the same range of emotions but being immature, it's just far more exaggerated.
It does take a lot of energy to follow through with this though - and I know from personal experience that that can be hard when you are feeling down. (I gave in on Thursday night btw when I absolutely shouldn't have done - dd protested illness and she was jumping around five minutes later eating an ice cream!!!)
And don't be down on yourself for your dd not being able to swim aged 5!!!
Loads of dc can't at that age. I even think there is some school of thought that many dc don't have the proper physique or coordination until aged 7 or older. It will come given time!!!
Take care and good luck x
And sorry for the essay 