My husband also has a big family that seems to be glued together for all events, birthdays, holidays, etc. My family was always just my parents, and my siblings, and me, sometimes our Grandparents or an Aunt & Uncle. We had time to really establish a close bond because it was a small gathering.
Being with all of his family at once is very overwelming to me. I always feel like I never get to have a "real" conversation with anyone, because there are so many of them. I have actually spent a Christmas eve where I only got to say hello and goodbye to his Grandmother.
My personal opinion is that you and your husband are the core of your family. You need to create your own traditions for holidays, especially now that you have a child together. You need to work on the core unit of your family (you, your husband and your child). This means taking time on weekends and holidays to do things within your family unit. Establish ground rules, like we stay home on Sunday's and do go to visit anyone - then they know not to plan the multi family B-day parties on Sundays or we won't be there. We also don't leave our home on Easter, the rest of my husband's family all gets together, but we are establishing our own Easter tradition with our children. Same for Christmas. We invite family members (different ones each year) to celebrate Thanksgiving with us. We still attend some of their big gatherings, but we pick and choose those that we will attend and those that we skip. My husband backs me up 100% on this.