Tough it out! Those two year olds can be VERY manipulative, lol. But if you give in, you are only setting yourself up for a lot of drama.
But I agree with the poster below - DO NOT 'sneak' out. You know that your son is safe and loved when he is with grandma, in his crib, etc. The only way HE will learn to be confident in that situation is to be IN it.
Try getting your mom or MIL to help. Have them 'sit' with your son and leave for five minutes at a time. When you leave, give him a kiss and say 'Goodbye. mama is going out for a little bit, but I will come right back and grandma is going to stay with you.' Don't let him hang on you and don't cajole him or make a big thing out of it. If he cries, see if grandma can hold him, but be kind and firm- Just GO.
Come back in five minutes, greet him happily and say "See? Mama told you she would come back and I did! Did you and grandma have fun?". Do this a few times.
Then go away for ten minutes at a time. Repeat, making the time frame a little longer, so it becomes more fun,like a game. Always praise him for being so GOOD for grandma and having fun and say " i told you I would come back and I did!" (this will take the whole afternoon)
Make sure your caregiver volunteer has a lot of FUN things to do- a favorite snack, a special cartoon, toy or book- whatever your child really likes and finds interesting right now. Make being with grandma JUST as much fun as being with mom!
He will eventually get the idea, it just might take a few afternoons of this. I know it is SO hard when they are crying for you. But just giving in all the time is not really going to do him a favor. Besides, as frustrating as the crying can be, grandma will love him anyway and has probably had to deal with this kind of thing before! She will keep him from getting hurt and that is the main thing. Sometimes you just have to wait it out- but this way you are still leaving, but also reassuring the baby AND teaching him.
In the end you will be glad - it will make preschool, running errands, maybe even a weekend away for you and daddy while the kids are with grandma?- SO much easier and happier for the 2 year old and everyone else involved! good luck!