Only rides that have restrictions do it. We never had any problems doing it on any ride, but our last trip when we went to do it on POTC because the ride just scares my daughter, we were told it could not be done on this ride because all ages could ride it. Most of the other rides we had done it on had the height restrictions.
The rules are different on different rides, so your best bet is to find a CM near the entrance and tell them what you want to do and ask what you need to do. Some rides your whole party needs to wait in line and then the first parent rides the ride while one waits and then they immediately switch. I know Star Tours is like this. If you have other children, they will get to ride with the first parent and then get to ride again with the second parent. Other rides give a fast pass/immediate board pass to the second parent so they do not have to wait in line. The fast pass/immedite board pass allows the second parent and up to 3 guests to board the ride at a later time. It does not give a specific time. We received one of these at Soarin and Expedition Everest. The passes also do not have a specific date on them so I am not sure if they can be used on a different date. On our last trip, we got the pass and then before my husband could go back a terrible thunderstorm came through and the ride was shut down so he never go to use it. When he went to discard it he realized there was no date on it, so if we don't lose it before our next trip, he may see if it is still valid.
Hope this helps.
