A males point of view, showing your ass purposely, NO!
Pretend that you think you have a splinter in your butt and ask for his help. Drop your panties and ask him to get it out. He will get a good look trying to find the non-existent splinter.
I don't know how you can show him your ass by accident.
If you truly want him to see your bare ass, just ask hime if he wants to see your bare ass. I am sure he is a horny old man. I am sure he will say he wants to see your ass.
So you simply put your back to him drop your pants and panties and show him your ass.
He will probably fondle your ass for a bit and then kiss your ass and then he will probably spread your ass cheeks and lick your little asshole. I know you will like that.
I assume you have a nice ass.
I can't think of a way for you to let him see your ass by accident. I would love to see your ass because I love ass.
Let me know what happens.
How about this? You wear a short skirt with no panties. You come through the living room and you drop something that will roll under the couch. When you go get the object, you get down on your knees and have your chest on the floor. Your skirt rises as you are reaching for the object and of course your skirt rises up and he sees your ass, your asshole and your pussy. He gets a boner while he is watching. You dig for the object as long as you want until you he has seen enough. He goes upstairs and he jacks himself off.
go in to the shower and come out naked
As an occasional "accidental" exhibitionist I can give you a female point of view. I have felt the way you do toward your boyfriend's father toward many men. It's very easy to flash your tits "accidentally" just by wearing the right clothes, but showing your bottom, and especially its middle parts is a real challenge to look like an accident. I think you have gotten some good ideas here already from other posters though they could be refined a bit. The splinter idea is great, as would be a bee or wasp sting, if you would scratch your bottom just a bit with a sanitized straight pin near your lower middle parts, just enough to get a little red and noticeable. The idea of picking up something from under the couch is great too, but wear a bath robe or towel. Going without panties with regular clothes looks very intentional. I love these posts because I'm getting ideas too. My own suggestion, based on my experience, is that it's a lot easier to flash your ass if you have a partner. A good example would be a short bath robe at a swimming pool or beach, or after a shower and your friend comes up behind you and pulls it up. Pulling off bath towels is also easy, and the friend can always apologize and say he/she thought you had something on under it. In your case, the boy's father wouldn't need to know it was a friend at all - maybe just a mean prankster. With a partner you can fake fights, play games, open changing room doors, do dares, and all sorts of fun. One last tip: Whatever you decide to do - practice it first and with mirrors. Visual angles and lighting as well as convincing "play acting" are very important. Good luck and I'm very excited to hear what you come up with and how it goes.
Try this: When your boy friends not there sometime make up a reason to take a shower. Once youre just wearing a towel ask his dad to help you get the water temprture right. Act kind of ditzy like you just can't get it right. When he sets it right lean into the shower so the towel falls into it. Then bend over to get the towel and slip around some with your legs apart til youre sure he got a good look. Then act all embarrassed and apologise.
wear a short skirt and go into the kitchen to help him with something and stretch up to reach something at a height there you go.
Tell us what you do though