I think you’re being really unreasonable, sorry. Funerals will normally allow people to show up regardless of the family’s wishes, due to Covid they have to be very strict. I can see why the funeral home wants to ensure all want to be mourners get to mourn, as close as to normal conditions.
The live streaming your children thing—sorry you’re being a bit precisou. There’s no problem with deciding you what to try to keep them off social media, etc but realistically they are being filmed every day in some capacity, you’re being very precious to blow up about this.
Also think of it this way: working in funerals must be one of the hardest, most emotionally draining jobs, you’re dealing constantly with death and tragedy, trying to ensure mourners get closure and keep various irrational, grieving people happy. They’ve been working throughout the pandemic, they’ve been dealing with people devastated at not being able to mourn in the usual ways, and then they have you coming at them on a high horse about your child social media policy and (sorry) your totally ridiculous problems. Yes if you feel strongly enough about it there’s no problem sending them a letter or having a conversation, but this whole attitude is unnecessary.
Sue if you want to, but you’ll look like dicks and I think you’ll have a very hard time in proving any damage caused. Yes things were not perfect here, but are you really amazed funeral homes don’t have cast-iron Covid policies for these very rare types of cirucmadtnces, when they have been working way above capacity for months dealing with all the pandemic deaths?!?