My son is a big kid, and we had this trouble early on, when he outgrew the Pack N Play. If you're going to a chain that has related chains nearby, like a Marriott/Courtyard/Springhill/Residence Inn kind of thing, I would talk to the manager of your hotel and see if you can get an absolute guarantee from him/her, even you if have to suggest that he/she obtain a crib from one of the sister hotels.
We had to say, "My son is over the weight limit. This is dangerous," etc., etc., all nicely, but with meaning. Hotels did accomodate.
Alternatively, you may need to find a different hotel.
We did rent cribs a few times, but when staying with friends and family, not hotels. Those rental cribs, like the hotel cribs, never were great...just a warning! You may prefer him staying in a bed, if you crib isn't great!
We moved our son out of a crib months earlier than our daughter, who is older than he is. They both were 2 when we moved them, but at different places on the 2-yr-old timeline. It made things so much easer, in some ways, with travel, not to have that too-big-for-a-crib issue.
Enjoy your trip, and good luck!