2001 Dodge Caravan Shop wants to replace pcm, need a 2nd op

Recently purchased a 2001 dodge caravan se. We first noticed that the check engine light was on but was told it was caused by a faulty oxygen intake valve and wouldn't affect the performance of the vehicle. Van drove fine, felt fine (no hesitating or vibrations) and sounded fine. All dash indicators work, brakes work, the vehicle was apparently well cared for but had spent quite a lot of time sitting in a garage.

Couple of weeks later, we noticed that the a/c worked fine. While driving. When idling, the a/c stops working but kicks back in as soon as we start moving again. It also seems to be warmer at slower speeds and gets colder the faster we go. Then, while idling as well, the van almost overheated (alarm dinged before it actually did).

We had three codes come up when we checked - one indicated that the battery had been disconnected, one indicated the radiator fan relay, and the last indicated a pcm problem (I can't remember the actual code numbers). At this point, we brought it to the shop. The mechanic informed us that although there was power going to the fans, and the fans themselves looked fine, they weren't kicking in so the pcm needed replacing at a cost of nearly $1000. We did NOT have it done at that time.

Move forward a couple of weeks, the fans still do not kick in when the van warms up but the weather's been cool enough that it's not a problem. - Figured we'd wait until we could afford to get the repair done.

But now we've fallen into limp mode. The van doesn't shift (automatic) up at all - we can go a max of 50 km/hr. It goes into reverse just fine, starts fine, sounds fine. But now we get another code P0700 - which, from reading, I understand means there's a transmission control problem but not necessarily a transmission problem.

So, my question is - does this sound like it is definitely the pcm? Would it make sense for us to try replacing the rad fan relay FIRST before committing to a pcm change? And would a faulty rad fan relay and overheating potentially cause the van to go into limp mode? Where would the air conditioning problem fall in here?

Thank you!