Sounds like a normal kid who's upset and worried about things because of the separation between mom and dad--and being put into day care with a bunch of strangers into the bargain. If you stop and think about it: How would you feel if you were three years old and all this were happening to you?
Taking toys away or giving him a time-out when he cries isn't going to make him feel less like crying, and at the age of three, he's pretty young to be told to 'man up.' What he's really asking for with that irritating whining is reassurance from you, but it sounds as though you might be to busy or too tired to get the message.
No doubt you're stressed by your life right now, but so is your kid. There are ways to improve the situation so that both you and your very young child will feel better and interact better with each other, but you have to reach out for help.
It couldn't hurt to join the child behavior community here to get some advice with the very common problems you are facing with this little fellow: