The three year old twins I know are very wrapped up in their own little world and have their own language with each other, to the exclusion of most others,although not mum and dad.
You perhaps seem to them as nanny who must be obeyed, as you chivvy them along to day care. It's not you they hate I'm sure it's just the situation - having to go to day care when all they want to do is play in their pyjamas?
You say you have been in tears so many times.
Is this in front of them? Probably not, but even so they will be picking up on your tension.
All I can say is, RELAX a little. They won't always be three, and they won't always be in daycare, and there is still plenty of time to be the doting granny you so want to be.
Alternatively just be an interestingly different granny.
Do things nobody else does with them, I used to take mine to the woods and build dens, play Cowboys and Indians, nobody else did this with them and they loved it.
I think doting has to come naturally, so it seems you are a doter, and your other half is not. Just let him be, you can't force it.