well first of all, pray on it, because even if your parents say no, God can open a door for you,
and i would recommend just talking to them about it, you don’t have to tell them what sin you committed, but you can try to make it clear that you most certainly do need to go, confession when in the state of mortal sin should be as soon as possible, it should never be put off,
and even though you must be respectful and obedient to your parents, don’t let fear get in the way of speaking with them about it, or human respect, because it’s God who you have to worry about most, He’s the one who is offended by our sins, and he’s the one who has the last say where our soul goes, so it doesn’t matter so much if your parents know you’ve sinned mortally so long as you can get back your sanctifying grace…although i’m sure they would keep it to themselves, because they do love you, and i don’t think you have anything to worry about in that area,
but just pray on it, and try to get to a priest as soon as you can, even if it’s before or after mass(don’t be afraid to tell the priest you need confession, that’s what he’s there for)
your parents have no authority to tell you you can’t go to confession, and if they know you’re in the state of mortal sin and say they won’t take you, then they sin themselves that way, but i’m sure they wouldn’t do that…
anyways, hope this helps, take care.