I am relatively new to churning. I've been churning Citi HHonors for about two years. I also travel a lot. So in the last two years, I've gotten 10 days at the Conrad Rangali for free.The basic room runs about $1000. I just booked my third stay. Between the churning and the Hilton bonus offers, I've done really well. I think Citi is about the last company that lets you churn the same card.

Chase is good, several different cards. You and your wife can have separate cards and so double the points/miles.

My suggestion is start slowly. Start with one card, meet the minimum spend and try another. I keep mine open about a year. Sometimes the cards come with benefits I want to keep. The Hilton fee cards (Amex and Citi) bring Gold levels which gets you free breakfast for two with each room. I would guess lots of hotels would include your children in the free breakfast. (But I don't know for sure.)

My other suggestion is to decide where you want to go, figure out how to get there, where to stay and then start collecting.

I think the credit card churning is winding down, but while it lasts, take as much advantage as you can. And don't charge more than you can pay off each month.