tamazaball: Why don’t you speak to your father and bring up the topic as if you would like his advice? For example: “Abba, little Rachel’s birthday is coming up, and she has asked me to make her a birthday party. Should I make it for her? If I do, then I think it would only be right to invite you and Ima, but you know…that might be awkward for both of you. What do you think I should do?”
If you present it to him as a dilemma, then he might just suggest one of the solutions recommended above and then there would be no problem! If he doesn’t suggest it himself, it would be a perfect opening for you to throw it out there as an idea that you just thought of. Ex: “Hey! This just occurred to me, etc….Do you think that might be a good idea?”
Hope that helps and welcome to the CR!