When your dad walked you down the aisle, he handed you to your husband. That symbolizes that you are grown, and in a bond now with your husband. I think your first loyalty now is to your husband.
It's sweet that you want to ask dad first, but I don't think it's needed. If you want to tell you husband, do it. He is there to be your pillar, your support. That's why you married him.
Everything the others said about suicide not needing to be a secret, I totally agree with. I also lost a loved one to suicide. Yes, the secret is dangerous since that level of severe depression is genetic. The family needs to know to be on the look out for mood disorders and to watch for signs of severe depression. There is no shame in this disorder. It's simply brain chemistry. Hopefully in time the family will get some education, and change their minds.
Maybe you'll be able to educate your father, and the info can flow up from there. This website may help:
www.afsp.org
They may find a support group that meets near them for "survivors" - the loved ones of those who have died by suicide. Your dad may want to look there for a group too. The website has groups, and lots of good info.
Hugs to you, Slippers