I've NC for this as I feel so guilty. I'm not sure this is entirely the right topic to put it in, but seems the best fit.
My 3yo has always been fairly anxious and nervous. She was a baby of the velcro high-needs variety, and at baby groups would spend most of them sitting on my lap soaking the room up with her eyes before having the confidence to pick up a toy etc for the last 5 minutes. She was/is very independent at home in terms of doing everything herself, but just had a high need for touch and an un-sureness about people who aren't me, DH or, since her arrival, DD2. We were always very responsive to her and very calm with her, even through the terrible twos, and I don't think we were PFB in terms of being anxious about caring for her.
As a 3yo now she is very anxious in social situations. She will always try and socialise with the adult in charge, never the children unless she knows them very well although she has an excellent relationship with DD2. She will still soak up the room. She struggles to separate from me at preschool drop off despite attending since Sept '16, and actually really enjoying it once I'm out of sight. You can see the panic in her face when it's time for me to leave 
She is nervous of getting things wrong, even though we have always encouraged her to give things a go and to keep trying if it doesn't work first time. The issues aside, she is also a very thoughtful, kind, smart, conscientious, and funny girl.
The last 12 months have been really tough for me for various reasons. It's been a culmination of a long list of things over the last 5yrs really, but I've hit a bit of a new low. I had counselling which finished a year ago and everything felt a lot better, but another blow has knocked me back again. With this my patience is shorter and some days I'm really snappy, particularly when I've been up a lot in the night with the DCs or they are having a particularly challenging day. I'm trying very hard to keep this in check, but it's sometimes impossible or catches me off-guard. I hate that I'm doing it. I try taking myself off when I feel it building but usually within 30 seconds either my 3yo or 19mo (usually both!) are hot on my heels 'Mummy'-ing me. If I shut myself in a room they bang on the door and shout until I open it which is more stressful than whatever I was struggling with before. I feel like I've lost the 'fun silly Mum' to be 'grumpy stressy Mum', but I'm making a huge effort to get myself back.
The crux of it is though I think my snappy-ness has worsened my 3yo's anxiety. I feel so guilty. How can I try to reverse the damage or is it permanent? I've always apologised to her for shouting or snapping when I've done it, and then explained the issue in my previous calm way, but of course by then the damage is done. I don't want her saddled with the lifetime of anxiety and depression that seems to track along the female line in my family.
I also have always been more confident around adults, and struggled to relate to/get on with other children as a child myself. As a result I didn't ever have close friends until my mid- to late-twenties. It was lonely, and I don't want that for DD1.
Are there any other things I can do (in addition to adjusting my own behaviour) to lessen the anxiety and grow her confidence?
DD2 is a completely different animal BTW, not a shred of anxiety there.
Any thoughts or advice is welcome please. Hopefully my ramblings make some sense, I should of course be asleep but my brain is running in overdrive.