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Why doesn't she want to? I would explain to her that periods are part of life. About 12 or more a year, that's alot of time to miss out with dad. If she doesn't want to go - you or her need to tell him the truth. You can't lie up to12 times a year. I'm sure he would understand but I'm sure he would be hurt too. But by talking to dad you might be able to come to a compromise or sort out a few things to help her stay be a little more comfortable eg bin in her room, a little more privacy, a bit of understanding if she's lethargic or not up for physical activities, and if she goes make sure she has a period kit including a heat pack, plenty of pads/tampons/liners/nappy bags, block of chokkie, do not disturb door sign, dark coloured towel, lots of knickers etc
Speak to dad, keep it discreet and encourage your daughter. No reason for her not to attend.
Speak to dad about it and sort out a compromise. She might feel uncomfortable spending the night, so maybe they could just do a daytime thing on those weekends, and dad could play along with the “sleepover” she has with her friends or the “family arrangements” early the next morning. Get him to put some paper bags in the toilet with a bin, if she would be comfortable with it even get him to put some pads in the bathroom for “just in case as she is at that age now”, neither of you need to tell her the truth of why he is doing these things. I remember at that age feeling very uncomfortable staying with my dad when I had my period, a lot of hiding pads and taking them back to my mum’s house to throw them away. It’s not like my dad shamed me or did anything, but it was just awkward.
Definately tell the dad. I’m sure he’d understand. If you don’t give him a reason he’s going to think you’re withholding her from him and it can cause big arguments. Be honest.