As a parent, I cannot stress how helpful having family support with small kids is during training. Yes daycare exists, but particularly in the first 6-12mo kids will be constantly sick and you cannot just call out 2-4 times a month (literally) because your kid is sick. You always need a backup plan, and if the backup plan is NOT "a member of my family is going to watch my sick kid" then you sort of need a backup to the backup plan. This was no joke probably the single greatest stress that my wife and I had when we started our family during my fellowship.
So this is where you need to have a serious conversation with your girlfriend--first of all, how committed are you two? Are you getting married, or if you're not the kind of couple that "believes" in marriage then have you talked about long-term goals and specific timelines for achieving those goals together? If you really do want to start a family during residency, is the childcare backup plan that your girlfriend is going to watch the sick kid? If so, is that feasible with her own life and career goals? And would she have an expectation that you would "pay her back" down the road when you finish training by doing something to support her?
While personal growth is a worthy and important goal, when you're in a committed relationship you really have to consider how your choices will impact your partner and potential family. Not saying you should or shouldn't go, but I would not just take "I support your decision" at face value. I'd really try to visualize what your lives together would look like either if you stay vs if you go.