Badges not triggering for Sims 3

All of those should work but there's a few things that can mess stuff up:

• Switching active households while attempting them, can reset those to zero even if you switch back afterwards
• Some don't trigger if you use a creature or supernatural Sim to to them.

Don't have any other suggestions as to try again with a fresh Sim (maybe even start a fresh game just to do the challanges.

No, saving and quitting is fine.

I don't have another solution and yes the badges can be a pain. I wish they made a way for us to check how far we are with the long running ones. This way one could find out what is not registering.

The most likely problem with Head of The Family is the grandparent isn't considered 'Head of the Family' in the backend of the game.  This tends to become an issue if you have been running a household for multiple generations. The sim you are giving the 30 grandchildren to needs to be the longest living sim at that resident. So anybody who has lived there long is considered the 'head', when they go, they pass the torch.  I hope that makes sense.  I never changed active household while doing, which I've heard can cause problems.  What I did, to deal with all the children, was age up one quickly and have them move out with as many of the other children as possible.

Chances are, there are strange little things like this preventing you from getting the other badges also.  One I had was selling the harvest to the shop for $50k or whatever it was.  Turned out it was because I owned the store so the sales didn't actually register, I could have sold harvestables untill I was blue in the face or to the value of 5 mil, still wouldn't have registered.

They require so many little details you wouldn't normally think of to regiser.