Has anyone checked the fluid? If you have developed a leak and the fluid is low enough, the transmission will slip. Don't go by whether there are any "puddles". You can still have a leak without ever seeing any puddles. Furthermore, you say that it often returns to normal after driving for a while. This would be consistent with low fluid. Transmission fluid expands as it gets hot. So the actual dipstick level is much lower when the car is cold than it is after it is fully up to temp. If you look at the dipstick you will see that there are multiple marks on it that vary according to temp.
If you do just have a minor leak that has drawn down the fluid level, now the surest way to kill it (if you haven't already) is to drive it while slipping. You will cook the thing with heat and extra wear on the clutches. If you find the fluid level low and bring it up to level and it drives normally then you can just drive it to a shop. If you add any fluid you use Dexron fluid only! If your owner's manual says Dexron III then anything on the shelf that is labeled Dexron or "Dex/Merc" is fine. But if it says Dexron VI, the bottle must be labeled Dexron VI. Dexron VI is good either way since that is what GM now recommends regardless of what your manual says. It replaces Dex III.
This is one reason no one can tell you anything by phone (or by web without full info). Another reason is that what the transmission is doing is intimately connected to sensor information about what the engine is doing. A problem with, for example, the throttle position sensor, MAP or MAF can provide incorrect info to the computer which then results in incorrect line pressures inside of the transmission.
There is nothing simple about any of it.
The issue with AAMCOs is that - well, some say it stands for "All Automatics Must Come Out" - meaning that it doesn't matter what the issue is, you will be told that you need a new transmission. Then the work you get from these places is often substandard. But this does vary - most AAMCOs are independently owned franchises, so their quality will vary a lot. You need to use some word of mouth about transmission specialty shops in your area. Ask around among people you know to see if you get any vague consensus on a shop that can be most trusted.