Are you obligated to stay for the next minyan's Torah reading?
According to the Rama (OC 55:2), if you are not the tenth man in their minyan, you are allowed to leave.
What if you're the tenth man in their minyan? The Mishna Berura (there, #12) writes that even if you are the tenth man, you only have to stay to the end of that particular section of davening. In our case, if you're the tenth man in the next minyan, and you answered Kedusha with them, you are required to stay through the end of Chazarat haShatz. However, since Kriat haTorah is a new section, you are not obligated to stay. (However, you should stay until they finish davening. See Mishna Berura 132:2.5)
(If you didn't hear that days Torah reading, you should stay, but whether you are obligated to hear Kriat haTorah with a minyan is a separate question.)
Can one participate in davening out of order?
Since the Shulchan Aruch writes (OC 236:3) that one should skip around in order to participate with a minyan, it appears that one not only can, but should participate out of order. And based on my above answer, which mentioned that there are different, separate, sections of davening, it follows that one should be allowed to "minyan-hop," saying some parts with one minyan and other parts with another. (However, I'm not a rabbi, and you should ask your local rabbi for his opinion on this issue.)