I used to work in a daycare centre and use some of those ideas for my snacks now. Some of the best are (I'm not peanut free) in addition to some of my own:
* Apple wedges with peanut butter (or peanut butter mixed with honey for dipping - almond butter would probably be fine too)
* Mixed fruit chunks with yogourt for dipping
* Home made yogourt popsicles - these are fantastic and can layer them for patterns!
* Graham crackers with jam
* Digestive cookie ice cream sandwiches (can make with any ice cream or frozen yogourt - just takes small amount....HUGE treat!)
* Bread sticks with ranch or cream cheese dip
* Funny face sandwiches (or crackers) - spread cream cheese on round crackers or bread, have small items for kids to make faces or make yourself with (alf alfa, olive slices, banana slices, shredded carrot.....whatever. ...try to keep it cheap)
* Watermelon is ALWAYS a big hit!
* Now sometimes we do crackers with dips such as hummus, babaganoush or something really different they've never had before....makes it adventurous for older kids.
* Impossible Quiche is super cheap and super easy (5 mins and a blender). Leftover's can be served as cold snack.
* deviled eggs
* Mini muffins (or half regular) - make up ahead and freeze - 30 secs in micro and snack is on
Kids aren't fussy about what is snack food and what isn't. I'll also bet that mother wouldn't pitch a fit over snack if maybe a little fruit was served with the mum mums and fishies. She probably just wants more balance....I'm betting it's her first child too? She's not tired enough to keep snacks simple yet
Now that I have home care, I typically have some plants the kids can get their snack directly from in the warmer months - raspberries and tomatoes this year. Parents always seemed impressed when they show up to find us sharing a bowl of what we've just harvested.
Good luck!