It is not unlikely that you will be the only mom in your PhD cohort. Though being a mom and a PhD candidate is unusual, it is not unheard of and does not mean you are less equipped than your colleagues, but it does mean you may have less in common than you did with your undergraduate classmates. It is hard to navigate the social world of graduate school knowing your other life waits for you at home.
One thing I found helpful in the beginning of my graduate school journey was not really talking about my family. I liked compartmentalizing my schooling and my home life so I could feel immersed in each. I also already felt different than the other students due to my outside commitments and didn’t want to make myself seem any “weirder”. I know having children is not something to be ashamed of, but I found it cathartic to pretend for a bit that I was just another student. You can make a choice to divulge as much information about your home life as you would like. If you choose not to talk about your children until you get to know your colleagues, this is OK. There are plenty of other things to talk about.
You also most likely won’t be able to attend as many social outings as your single and childless counterparts. You should try to attend some to get to know your classmates, but don’t feel obligated to attend them all. Many graduate student events occur during the day or early evening, these events are usually the more professional and important events to attend anyway. Try to get to know your classmates, even if you feel as if you have little in common. They can be important resources in the future and may just become good friends.