i have to add-your dog's death was not your fault. you tried your best to get her to the vet but things were out of your control. i am sorry your family was so insensitive to your dog's plight and to your feelings. i am also sorry you had to witness her last day. that sounded so traumatic. i know you would have saved her if you could have.
i also was consumed with guilt and grief after my pets died. i found saying out loud how i felt somehow lessened the pain. if for some reason you cannot stop feeling guilty, here is an article from petloss.com. Dealing with the Guilt in case it might help.
do hold on to the fact that those last few weeks of your dog's life was only a small fraction of her time on this earth. main thing is she knew you loved her.
so please be gentle with yourself. many hugs.