One is mine, one isn’t. Can and should I still raise both?

By way of introduction, I am a 34 year old single father. The mother of my child (25) decided a month after giving birth to my son that she didn’t have feelings for me anymore and called it quits. Our son is now three and a half months old.She has a two year old from a one-night stand that I am ridiculously attached to and consider to be my own as well. To this day, she still calls me the father of BOTH of her children. For the first month of our breakup, I would only have my son. But, for the last month, she has asked me to take both kids on the weekends, saying I’m no uncertain terms that it breaks her heart when I come and split the boys up for the weekend As you can probably guess, her guilt trip worked and I have since obliged for the past month, but not without reservation.My question for the masses is, am I doing the right thing here? I absolutely want to be in the older child’s life and love him like my own, unconditionally. And it goes without saying that my own son is my whole entire world, just as his brother is. According to his mother, he older child goes on and on asking about when I am coming back to get him almost as soon as I bring him back on Sundays.The relationship with his mother is another issue entirely; however, I am greatly concerned that I am being used as a babysitter. Especially since she’s made it clear that she doesn’t feel the same way for me as I do for her. I want nothing more than to be a family and make this work....mom has other ideas, and I am honestly very hurt that she up and left me a month after our son was born. I firmly blame postpartum depression, but that is an issue for another subreddit.But, back to the child that isn’t mine. Am I dong the right thing here? Or am I getting taken for yet another ride? I’ve had this conversation with myself and I am finding myself wavering between calling myself selfish for not putting a helpless childish first and calling myself stupid for being played for a fool.Your input is appreciated. via /r/Parenting https://ift.tt/2IDeobS