I have had a mini-14 since the late 80's mainly for managing cows and coyotes.
Excellent firearm and ditto on the simplicity/serviceability, has never jammed (EVER), and cost of parts.
This all being said, one of the best things I did for it was trade another mini-14 owner my wood stock for his adjustable poly stock straight across...he didn't shoot any more and I do.
My young daughter (who shoots a Mosin Nagant) hates shooting the mini-14, it is jumpy (although I have not added weight to change it's resonance like armymars suggested).
Our friends with ARs took my wife and daughter out shooting and they both LOVED them. Just like machinisttx indicated; adjustability, low cost parts, mounting systems; they couldn't believe it shot the same round.
I also have AK and SKS; although the round packs a lot more punch, for ease of use, accuracy, custom-ability, and female friendliness I am going to have to buy ARs for my women; pink and purple cammo of course

PLUS ONE for xxdabroxx.
I understand your concerns with the " social worker who would be horrified" yet I don't think you're giving her enough credit. If she is educated and already on board with coyote control then I think she would be most pleased to learn that your children are trained in the use, care, control and responsibility of a tool (firearm). Be proactive and not prejudice.
I'm certain you are a responsible parent, make sure your children see you model your concern for the neighbor's perception without letting her control your decision. Don't model crabs in a bucket.
I like my neighbors, coworkers and family and go out of my way to be a great friend in return. I also make no apologies for the choices I make with food, finances, firearms, etc. I make choices that are the best for my family with the information I have available through the filters of my experiences. There are members of my extended family who freaked when they found out that my daughter saw me castrate the family dog...not kidding. My daughter saw that I handled it gracefully yet firmly, and now models that same behavior when peers disagree with her.
I hope this helps, and thanks for bringing up daughters to respect and use tools.