Oh honey, I had this same experience with my oldest when she was the same age as your son. It's definitely because he's 2! I was just not able to enjoy being with her, and I felt so guilty that I preferred playing with and being around the baby. I had an epiphany when I was introduced to "Parenting with Love and Logic" by Jim Fay and Foster Cline. http://www.loveandlogic.com/ It's also on Amazon.com
Reading the book was great, but personal training really sealed the deal for us. I found a family counselor who is trained to teach love and logic to parents. She's also a parent herself, so she has some "battlefield" experience. I actually organized a small class for parents at our church. It has really given me the tools necessary to enjoy my child again.
I got the book and started trying to use the philosophy of giving choices and we had fewer battles, but I was still having these moments of rage and being fed-up and running-from-the-house-screaming when my husband came home from work, etc. After the class, and working with the counselor separately on some specific problems, our lives are sooooo different.
Parenting is a skill just like any other skill that we need to seek training on. It took getting to this point with my daughter to realize that. I mean, you have probably had some degree of training on how to use a computer...why not take a class on how to operate your kid?!
You have to remember that a 2-3 yr old is struggling with independence and desires your full attention. That is likely heightened for a middle child -- big sis gets to do everything for herself and the baby is getting all the cuddle time.
While you're waiting for Amazon to ship your book, try to pre-empt the explosions by giving him a little control over appropriate areas of his life. Let him choose his own cup and plate and fork, let him get them himself if he can. Let him pour his own milk in his cereal (We would pour it in my daughter's cup and then she'd add it to her cereal), give him the choice of 'do you want to take a nap now or in 3 minutes? "You may eat nicely or go to your room." etc., etc.
Also, a very important thing to have is empathy. When dinner time becomes a battlefield and your son has to leave the table, get dramatic (without sounding insincere) and say, "This is really sad. I know you would like to be with your family, and I really like it when we're all together, but it looks like you need to spend time in your room."
I still have the counselor's number if you want to call her. She is an independent counselor and does in-home training, but she's also affiliated with Cumberland Presbyterian Children's Home in Denton (www.cpch.org). They actually have several instructors who can offer Love and Logic classes on their campus as well. It's the philosophy they use with the children who live there, so they are experts at it -- their residents are from toddlers up through high school. There aren't many situations that they haven't seen and worked through successfully!