I mean, if you happen to have some heroin lying around, 50mg/kg should definitely do it and the rat would go out having the time of her life. Definitely weird to see, though. *Disclaimer- the highest dose I've ever used on rats is 10mg/kg and they were absolutely rigid and high as a kite. None died but I've heard of it happening- I suspect those cases were not actually heroin directly but suffocation from being SO high that they didn't move their faces out of their bedding. Hit me up for stories on what happens when you try to move a super high rat.
Otherwise, fork over the money and call it a kid cost. I've done CO2 ... once. I swore to never do it again. If you have the right protocol AND the right equipment, it can be peaceful but in my experience, that is rare. Cervical dislocation and guillotine are both fast and humane but pretty gruesome and if it goes wrong, it goes reeeeeeally wrong. *Disclaimer- I've never actually had it gone wrong when I was doing it but I've seen/heard it happen with others. *shudder* Also, I don't know where the average person can find a rat guillotine and cervical dislocation gets more difficult the larger the rat is.
Don't underestimate the emotional scarring from loss of pets. I'm still furious at my dad for leaving a window open that let the cat I grew up with out when she was recovering from surgery and also for getting and keeping a dog that was obviously aggressive towards cats... you can see where this goes. That was a decade ago and I was a full grown adult and I still resent him for that. You sound like you'll do the right thing, though- I like the lilac bush idea. Your kids will appreciate it. I hope if the event has occurred, all went well.
PS the cost of obtaining a pet is often the least expensive part of owning a pet. I've easily spent $15k on my 2 cats that cost $10 each when I adopted them. Probably shouldn't admit that here, but eh, I'd do it again.