Hi,
I'm also a 25 year old mom of a three year old with an active duty husband and am in the process of enlisting. For me, the career benefits, the lifelong experiences and the role model I'll be to my daughter by serving my country via Coast Guard outweigh my short term (and still current) worries about leaving her for 8 weeks. Of course I'm still a little anxious about leaving her for 8 weeks, but I try to focus on the big picture and how much it'll benefit not just me, but my whole family for the better.
Actually, there's a thread I posted regarding my concerns of leaving my daughter in this thread:
[
http://www.uscg.org/forum/?f=17&m=62768]Best wishes in your pursuit!