What do I do?

My boyfriend came home and suddenly broke up with me last Saturday after not seeing each other for 2 months due to him being underway, so I’ve been dealing with that. His mom messaged me 3 days later asking if I could still take her to the airport in May and pick her up in June since I just got a new job. I said “sure if you’re comfortable with it?” then asked if he told her what happened between her son and I, and she said “yeah, but we can still be friends!” I really don’t think we can? I’m not going out to lunch or coffee with you when your son wants nothing to do with me. It would make me look desperate, and I’m just trying to move on with life. I’m really not down to take her to the airport, but I promised her I would a month ago.

Not to mention he just left to go underway for a month again (yes he came home, broke up with me, and went back out). I wouldn’t be surprised if she tried to invite me over while he’s away, and I’m really just not up to dealing with this. I’ve already got suspicions he only broke up with me because he couldn’t take only seeing me once a month for the rest of the year, and he didn’t find it fair to me to sit around and wait for him. I don’t need to be feeding my broken heart by being around his family hoping by some miracle he’ll change his mind and take me back.