getting rid of lead in solder is much more of an issue for disposal of mass produced items and for people working in plants with paste solder than it is a potential problem for a home working person like most of us. I've had those blood test and in spite of soldering fairly frequently with the lead I do not have elevated lead levels in my body at all. The most important precaution you can take is to wash your hands after handling the solder. This is how it gets into your body when you get it into your mouth, or much more slowly absorbed through the skin if you leave it on your hands for a long time. Your kids will be safe as long as you keep it up on a shelf out of their reach.
It's the smoke and fumes from soldering that people tend to be afraid of, but there isn't actually any lead in the smoke. Even the highest temperatures reached by a regular soldering iron are so far below the vapor pressure of lead that it simply doesn't vaporize at those temperatures. You get a lot of nasty stuff from the flux and you should probably have a fan or a vent hood if you do a lot of it, but not to protect you from lead. That just rubs off on your hands.
If you do invest in the RoHS iron, make sure to keep it turned down or not use it with lead solders ever as they can reach temperatures where lead would start to enter the smoke.
I"ve done some work with the new stuff. It does take a little getting used to. I've ruined small components much quicker
For most of my just tacking things together I still use the old lead. But the new stuff seems to work OK. There are plenty of concerns out there from companies that dont really want to spend the money to upgrade their processes, but I think most of it is FUD. The Tin Whisker problem though, of tin forming whiskers that short stuff out is real and I've even seen that in some of the outdoor lights I put together as recent as a year ago! Be interesting to see what comes of that and if future formulations can get around it.
But depending on the amount of work you do, and your own ability to remember to wash your hands and keep your solder up on a shelf, it really doesn't make a dangerous atmosphere for the kids. You REALLY do need to wash your hands or you'll contaminate everything with lead!