I feel your pain!
10 months is a really odd age - and they do suffer incredible separation anxiety at that age.
My DS (who happily went to nursery 4 days a week from the age of 6 months) had terrible screaming fits when I left him there at 10 months old even though he had been going there happily for over 4 months!
There is nothing worse, you feel terrible, absolutely terrible - and it's no frame of mind to go back to work in. But life goes on, we go back to work after maternity leave, our kids go to a childminder / nursery, and somehow, some way we find a routine that suits everyone.
How many days will he be with the childminder a week? Hours? Is he full time?
My DS still screams now when I leave him at nursery (he is 29 months old now!) - But 5 minutes after I go he is absolutely fine, joins in with the other kids, has a great day and greets me with a big smile when I come to get him, and usually doesn't want to leave!
If I were to give you any advice it would be to stick with it. I think its a bit unkind of your childminder to stay he's the worst case she's ever experienced! It can take weeks for them to settle, I would say anywhere between 4 and 10 weeks is normal. I know, it sounds like a lifetime, but it really isn't.
And please don't worry about the stress on him. He is distressed, not stressed, he won't remember a thing about this later in life, so don't think he will turn into an axe murderer because you are a working mum!
I feel for you, there is nothing worse than leaving a screaming child who is holding his arms out to you - but it really does get better. I promise. And then what do you have? A happy mummy and a confident, independent child.
It will work out, I'm sure.
Hugs xx