I would be asking my DH to support me in my parenting decisions. The last thing a toddler needs is blo**y coffee! Caffeine in toddlers is a crazy mix!
I would consider apologising for losing it, explain that you are very frustrated that she refuses to listen to you, you have asked her repeatedly not to allow your lo to drink coffee, yet she continues to ignore your wishes! I would say that if you cant trust her to respect your parenting wishes when you are right there, then there is absolutely no way you would be prepared to leave your lo in her care.
You are the Mother here and you deserve to be treated with respect. She had her time being Mummy to her own children, this is your time now. Whilst she may have happily allowed her own babies to drink coffee, you are not and you have very good reasons for that! Whats next, wine or vodka? Tell her that you don't need to take abuse or name calling! If you are both going to get along then she owes you an apology just as you owed her an apology.
I would also let your DH know that as your DH, he should fully support your parenting decisions! He should make it very clear that giving your toddler coffee is absolutely NOT acceptable! If he doesn't agree with you, he should wait until you are alone to discuss it, although I would think it pretty self-explanatory that giving coffee to a toddler is not a good parenting move!
How is your relationship with your MIL outside of this outburst? Do you ordinarily get on? Is your relationship with your in-laws toxic? If it is then I thoroughly recommend the book Toxic In-laws by Susan Forward.