We haven't started shopping for this Christmas yet but after reading your post how both sets of grandparents would not like the idea of throttling back on gifts I had to reply.
Since our children were babies, my parents would give them generally 1 decent sized gift but the majority of their real gift was $ invested in a custodial account. Every Christmas and birthday they put around $200 in the account. They did this for all 4 grandchildren and now with 2 great grandchildren, my brother's grandchildren. By NJ law, (varies in each state) a custodial account must be turned over to the "child" by age 21. The custodian, in our case my father, does not have to claim interest earnings as income. Most kids don't have enough income to need to file a return so it was a non-issue for us.
Our kids never knew this was happening. They would still get a nice gift from my parents, let's say something like a digital camera or electric car, depending on their age.
By the time my first born was ready for college, my dad told him he'd divide the balance in fourths and each year he'd contribute 1/4 of the account toward college rather than empty it the first semester. At the time it was around $16,000 so he gave him $4000 for his freshman year. Good thing because he only spent 1 semester at college.

By the time he turned 21, it grew back the $4000 that was pulled out and then some. It was almost $18,000. I was so afraid he'd blow it on stupid things and we had a good conversation about what a generous gift this is, etc. He paid off the $3000 in student loans he had, kept about $500 in his regular savings account, and invested the rest in 2 Vanguard accounts: an regular investment account and a Roth IRA. He is 23 now and is quite a saver and the mutual funds we chose together (which dh and I opened same one for ourselves at the same time) have done very well since we opened them. His savings are well over $30,000 and he loves the power of compounding interest and watching it grow.

I convinced him to please don't tell his younger brother who will turn 21 next spring. I really didn't want the idea of a big chunk of money coming his way to sway the good decisions he has made. He has worked hard to pay off his 5 yr car loan in just 1.5 years and he may not have been so motivated to do so if he knew. Because his account has had more good years in the market compared to his brother, his is over $21,000 now. My dad is so excited to give it to him

and every time he sees me, he has to tell me the latest balance.
Anyway, sorry this is so long but depending on the age of your children this might be something to suggest to the grandparents. I see my coworkers spending hundreds on their grandbabies on BS stuff that will end up at the bottom of the toybox one day. Even when we try hard to not spoil our kids, they still have a lot so why intentionally shower them with so much? Didn't we all watch the original Willie Wonka and see how ugly spoiled kids are? "Daddy, Daddy, I want an oompa loompa and I want it NOW!"
Someday if/when I have grandchildren, I plan to do the same thing.