It looks like it might be persistent. Not sure since I don't have an Xbox, but there is a Q&A thread at the minecraft forums.
I have been following the main GeekDad site for a while, just joined the community section, and came across this thread. It is good to come across some fellow Dad Minecrafters.
Some contributions to the topic:
1) MINECRAFT ON YOUTUBE-
Like you guys, I frequently have to show them muted, due to the language. That's our rule, If dad has not heard them before, the sound stays off. Some good ones out there for you to check out are:
+ MincraftWB (The Luclins) A family that does gaming together. A lot of Minecraft stuff and relatively language free (He places a warning if there is any content like that) I really like these guys; a mom, dad and a 12 year old son. They are the ones that inspired me to get started in Minecraft.
+ Paul Soares Jr (Survive and Thrive) A businessman and dad. The original Minecraft Youtuber. A little dry, but he definitely makes me smile. Absolutely no swearing, and a truly nice guy.
+ AdamzoneTopMarks (Minecraft Chap) Or as my boys call them, the guys that talk funny. Their fast paced Brittish accent comedy hardly let's you come up for air. I have to date heard no cursing. They do a lot of MOD reviews and are a lot of fun.
2) GOOD SERVERS-
+ PunchWood.com Paul Soares Jr's server. Very popular, a lot of folks who apply for whitelisting. I have heard that it is good, but have not tried to get on myself.
+ IndieSquish This is hands down the best server out there. I rarely play on any others. It is a mostly vanilla SMP (Survival Multi-Player) server with just a couple helpful plugins (like home and lock chests). Absolutely no swearing or griefing. The whitelisting process is long, but it truly keeps out almost 100% of the hooligans. It is really worth it, and I would highly recommend it to anyone. Very well run.
3) OUR PROJECT-
My two sons (4 & 5) and I do a webshow together called KidAwesomeTwo (it stands for two awesome kids, one lucky dad). The first series came out a few months back, but once daddy gets his new computer should be coming very soon, we will be doing a major reboot of the series. I would love to see what the others think, and hear any good ideas or suggestions for the upcoming shows.
I'm sorry I spouted all that info at you at once. Maybe the GeekDad Server will become a reality some day. I would love to meet you all "in game".