We were told never, ever to put our cat out at night. I would question why your vet told you this.
I live with four cats one of whom is very timid and nervous and hates being groomed (total nightmare it takes the three of us - one to hold, one with treats and one to actually comb!) Maybe you could try keeping her indoors, leave an empty cardboard box around, (not too deep) and chances are she'll get inside it and just stay there, all of ours love boxes even carrier bags (which is to be discouraged) I'm afraid all you can really do is have lots of patience and treat her kindly she will eventually learn to trust you and feel safe I'm still having trouble with Lou but she's coming around and sits and snuggles into to me and she also lets me know when she wants her ears tickled or just stroked, so far it's been 4 years and while she comes to me she quite often runs away. Patience, you'll need lots of patience