There's a couple of problems with "in a home".
"in" means "inside" in this context, whereas "at" means "at the location of" - it's a bit more general. The delivery will be to the door of the house, it won't be inside the house, but it will be at the same location. So, "at" is better than "in".
The next problem is "at a home".
"A home" is too vague - it makes one think of a specific place, eg someone's actual house, but doesn't suggest that it will be the customer's home. Saying "your home" or "the customer's home" fixes this problem by specifying whose home the delivery will be made to.
You can alternately just say "at home", which is also general but is a familiar phrase which people would take to mean "at their own home".
"No matter if your delivery takes place at home or in the hospital ..." seems fine to me.