Your teen doesn’t need your guilt, but they do need your compassion. Being compassionate means not buying their feelings away with ice cream and gadgets, but you let them talk about whatever they want to while listening without judgment or putting your feelings before theirs. This is important, and this is very hard. There’s a reason you decided to divorce and your teen may not know all the details of that, but they can be allowed to vent their feelings about how their life has changed. So yes, stick to the rules, but be willing to look for opportunities to give them a break when it has been a heard day emotionally for them. I think you understand this. After all, you have emotionally rough days too. Your willingness to do this will tell them you understand the magnitude of your decision on their life; and instead of anger you could become more close. This is the gold you are looking for because divorce is about trying to be a happy family and strangely enough sometimes divorce is what brings that happiness.
Being a parent means sometimes you have to make really hard decisions and it also means that the impact of those decisions isn’t just about you.