If you're worried about the dad, then I probably wouldn't say anything to him. Just better to leave it at that for the time being and if you can trust your mom not to bring it up.
As for the mom, I guess if you want to do it face to face just sort of find a time to isolate her and just bring it up in a really humanstic way. Just tell her that this is something that is a very big deal to you, and her support means a lot to you etc etc. Hopefully she will understand your sincerity and also acknowledge the situation, although that can take some time for it to sink in after the initial phase. Just remember everything takes time, so don't expect anything instant, and views can change over times for the better or worse, so mentally perpare yourself too.
Good luck if you choose to do it