I know or know of several Aspie parents that are wonderful parents. If there were some evidence in your children that would cause people to question your suitability as a parent, I can see an investigation happening but, just being diagnosed isn't cause for anyone to think you would be a bad parent.
Obsessions don't always take an obvious form or mean you engage in them for hours every day. One of mine is food and cooking but, I don't cook huge volumes of food or spend all day cooking. Where my obsession comes in to play is learning new recipes, preparing five star quality meals for myself, friends and family, always thinking about a dish I want to make and, what occasions it will be best served for, how I can change up favorites to make them new and exciting and, if there might be a new way to prepare a certain food.
Music is my other obsession and, while I obviously don't write or perform music fog hours on end, I'm always thinking about it, working on a new song in my head or silently singing a familiar tune. I'm always aware for what is going on with fellow musicians I consider friends and, looking for ways to make my music a force for good in the world.
Just because it's an obsession doesn't mean we do it all of the time, or even every day but, we do think about it constantly and relate anything we possibly can to our obsessions.