Welcome to SR, this is the greatest place and glad you found us. I am so happy your parents found recovery.
Sorry, but in my opinion relationships are difficult. The recoverying alcoholic is fragile and may take years to get a good hold on dealing with life on life's terms. Also they can relapse as you know.
You are already walking on eggshells due to your knowledge, if possible I would let this relationship go.
Sometimes recovery is forever full time for some.
This is just my thoughts, Take what you can use and leave the rest.
Caring, understanding hugs.