Read the actual policy - it has to be written out. Here is what I would expect:
Costs for you apply to your individual deductible and the overall family deductible. Once you pass either one, further treatments are free
Same for your wife.
Your kids (or anyone else on the plan) cost until the family deductible is reached. You and your wife's costs pay down both: individual & family. Kid payments only apply to the family part.
Say your individual deductibles are $1000 each, and family deductible is $2000. They're usually higher, but lets simplify the math.
You pay $600 for hair extensions. Result:
Your remaining deductible is $400. The family deductible is $1400 now, and your wife's deductible is still $1000.
Wife has a $500 procedure done for lipo.
Family deductible is now $900. Your deductible is still $400 because the family cap hasn't fallen enough to reduce your cap. Wife's deductible is $500 because the family part hasn't fallen enough to limit it.
You have another $600 procedure done. Permanent underarm stop-sweat.
You actually paid $400 which fulfilled your deductible. The remaining $200 they picked up. Family deductible is now $500. The $400 you paid reduced the remaining family part from $900 to $500 (the $200 they paid for you doesn't count - only your payments reduce deductibles). Wife deductible is still $500 because the family cap hasn't fallen below her personal cap.
Your kid has a $100 treatment for acne.
Your cap is already satisfied - your further treatments are free for the rest of the year. Family cap is now $400. Wife cap has been reduced to $400 because the family cap is now lower than her individual cap.
Assuming there are two people in your household, there isn't a difference. You'll each pay up to your $1000 and the rest will be free for the rest of the year.
If there are kids in the mix, their payments would reduce the family cap. Kid payments against the family cap will eventually reduce your individual caps.