First Idea:
*Sighs*
Hunting is different that caring for cubs. Much different. So why does a broodmother earn hunter Exp for caring for cubs? Why not, have two different Levels? Like, Regular levels gained from hunting and items, and a second, lets call them 'Broodlevels'. Brood levels are gained from cub caring, and they'll have their own little leaderboard and the such.

Items that could boost broodlevels:

Human Doll: How cute! Maybe it could teach your broodmother some about caring for cubs?
Egg: Maybe if you told your lioness not to break it, she'd keep a close eye on it?

Oh. And Brood levels add onto my second Idea. Keep reading!

Second Idea:
Now... If we are talking realism here on Lioden, we know this.

Lions make mistakes.
So why not have a broodmother make a mistake?

It won't be awful, nor will it kill a cub. It'll be rare.

My Idea is this:
Every now and then a broodmother will slip up, doze a little to long, or take their eyes of your mischievous little devils. A cub with wander off, and will get into trouble, lowering their survival bar. A broodmother will realize her mistake, and care for the cub, raising the bar. (Like, if a cub lost 20 survival, the broodmother care will raise it to only loosing 10 survival.)
From that mistake, she will get a little experience boost, since she will learn from her mistake.

Oh. And the higher the level lioness, the less likely she will make a mistake. Like this:
Level 1: 1/10 chance of a mistake
Level 2: 1/15 chance of a mistake
Level 3: 1/20 chance of a mistake
Level 4: 1/25
And so on and so on.

Personality effects on mistakes
Lazy and Unreliable lionesses will be more likely to make a mistake. Those two personalities, instead of having a starting chance of 1/50, have a starting chance of 1/40, and gain an extra 3 instead of 5. So, they would go:
1/2 = level 1
1/5 = level 2
1/8 = level 3
and so on and so on
((FYI, my own broodmother is unreliable. I would be putting my own self at risk if this was implemented.))

Nurturing Lionesses get more experience per day, and are less likely to make mistakes.
Cuddly Broodmothers can go up to broodlevel 17, and give the cub +6 training per day.

Ok. For those of you who are like 'Hnnrrrgggg no support I want cubs safe under broodcare!!"
Big Point:
It is almost impossible for a cub to die from a Broodmother Mistake It takes off 20 of the bar, then the broodmother fixes the little cub up, then lowering the loss to 10. In order for a cub to die from broodmother mistake, a broodmother will have to make a mistake ten times in a row. And with, at maximum, a 2% chance of a mistake happening, it would be absolutely crazy if a cub did die from this.

EDIT:
Since some people have raised concerns on why this should be added, what if it added cub training? For example:
At Broodlevel #5, cubs protected by the broodmother gain +1 cub training every day, with the amount of of cub training added going up by +1% every two levels, with the maximum being 5% cub training every day at broodlevel #15.