If you genuinely feel you can't cope, don't write off the option of rescue - there are rescues who will take on dogs with behaviour difficulties and place them in homes with owners who are experienced.
Don't feel you are letting Dora down by saying you can't trust her in your home - and don't feel that PTS is the only alternative.
There are members on here who are involved in some of the rescues who would be willing to find Dora a new home if that's what you feel is best for her and you. You are obviously committed to her and your love for her has shone through in all of your posts about the difficulties you have had with her. You are honest enough to know that your feelings and emotions are transferring onto Dora and making the situation worse, and you are not sitting there saying that she is an unmanageable dog.
It may be that this incident is just still too recent and your emotions just too raw to make a long-term decision about her future, and that posting has helped in some way. But if, once the dust has settled, you still feel you are not the right home for her, no-one will judge you for that.
I can't imagine how you are feeling at the minute - it must be heartbreaking for you to even be considering this - but hopefully the knowledge that there are rescues that would help (and not just PTS) will help you come to the right decision for her, you and your family.
