You know, my mother told me the same thing with my first child. But I read "Happiest Baby on the Block" and "The Baby Whisperer". Both had very good suggestions on dealing with cranky babies. My daughter was a little tempermental. But these books (especially "The Baby Whisperer") taught me exactly to put her on a schedule....a schedule for EVERYTHING. By doing this, it eliminated her worry or fears of what was coming next. She never really cried after that from hunger, for example...because I was always a few steps ahead of her. Even naps and night time were so much easier.
I'm not sure if any of this will help you or not, but strict schedules really seem to keep cranky babies become a little more predictable. It's also easier then to tell what they might be upset about.
As for the Grandma's, just handle that with a bit of grace. I'm sure you'll do fine. A smile will go a long way. Just remember, there's a maternal instinct so strong to help your child when they're upset... no one can tell you to supress such feelings. It wouldn't be natural. When my daughter was very little, my breasts would leak every time I would even SEE another baby crying! It's a physical response as well as emotional. Your heart is certainly in the right place!
Good luck to you, I'm sure the "spoiling" concern will work itself out. Oh, and if your child is fearfull of strangers (as my daughter was), acknowlege that. Explain to everyone that it's now their fault, and it's just a phase...(yadda yadda yadda) and he'll grow out of it. Then take him away. It's not worth (in my opinion) the undue stresses, when it's a phase that will pass. Plus, you want your child to know that if he feels unsafe (no matter how rediculous it seems)that you will help him feel more comfortable, and with that, will come confidence.