I couldn't read and run.
First of all, I'm so sorry for your loss @Restart10. Losing a baby must have been extremely traumatic for the whole family, even the youngest toddlers pick up on these sort of things. Are you getting support e.g. counselling for yourself if this might be helpful? 
A few things stand out. I won't tip toe but say it outright, it reads to me like you are absolutely feeding your dd's anxieties. By letting her dad speak to her on his way to work, you are pandering to her, she needs to learn that sometimes things feel sad and that she overcome this. However, talking to her dad in this way fosters a dependent attachment and is not good for her or the overall family dynamic.
Look at your own anxieties and your relationship with your dh, you dc will copy and absorb so much based on this. Sometimes tough love is required too, at the moment you are reinforcing the image of your dd as anxious, helpless and fragile. But unless she has additional needs, she is not that, she's probably a tough cookie, if you give her the chance.
I'd try and build her up using CBT techniques (there are lots of books on Amazon) and the best thing that could happen to her is to make lovely friends. Let her try out new activities, Rainbows, a team sport, art club. What are her interests?
I'd avoid changing school again, let her find her way, she is still very young and will most likely grow out of this.
Try to reassure her when she has worrying thoughts "most people feel like this sometime, it's ok and normal." or when she sees a problem "let's see if there is a solution" turn it into a game "tell me 3-5 solutions to this problem, they can be crazy, fun, ridiculous or serious" it might help her shift from focusing on the problem to helping herself. "Why do you want to do this perfectly dd? Humans can never be prefect, if we were perfect we'd be robots and we wouldn't want that would we?" "Every problem has a solution dd, what do you think you could do to make this (x,y,z problem, worry) better?"
Schedule time for worry but don't let her tell you her worries all day long, it will zap the happiness out of you! Tell her she has 15 minutes each day to talk about what worries her, then complete this by thinking of 3 things she is grateful for any why. Let her say these things out loud, slowly help her shift her mindset from feeling helpless to feeling in control (or reassuring that sometime we are completely not in control and that's ok). I wouldn't bother with worry beads, dolls etc in mind they all just reinforce that something is wrong and anchor that sort of self belief.
Your dd is at an age where is still very receptive to this sort of guidance from her parents.
Play therapy for years at such a young age sounds a bit excessive, my concern with this sort of thing is that it might reinforce her image of herself as someone who needs help to cope, she gets attention for feeling anxious. Unless she has Autism or special needs this should help her move forward. If you try this and nothing helps, try and have her assessed. Stop focusing on her fragilities and start building her up, let her conquer things and do things for herself.