Hoping someone can give us an idea of where to even start with this.

We have a 2002 grand caravan sport edition. Since the weather has been getting colder we have noticed some strange power issues in the van. It will rev up (as though it is in cruise control and going up a hill) for no reason. Or it will seem to lose engine power for a few seconds, lug and then be fine. But the strangest piece started happening last week. It loses auxiliary power. Tonight when we turned it on the box that indicates what gear you are in was gone, then every fear had a box and. Then it was normal and then the box was gone again. The radio kept flicking on and off, the power windows would not work and while we were driving we completely lost our lights. It has an emissions code when you plug it in to a reader which we assumed had to do with the fact there is a small hole in the top of the gas tank we have yet to fix (it's miniscule and in the full tube)- the check engine light was on and again we assumed the two were related but since we put the reader on it Saturday that light has gone out. The auxiliary power problems only happen when it is cold outside. All the connections seem fine, it turns on with no problems and it has a new battery. The loss of power and the chugging it sometimes does is getting a little worrisome. Anyone have any ideas what could be causing these issues or where we should start looking? My father in law is a mechanic and he was at a loss but he also hasn't seen it do any of this because by the time he sees the van it has earned up and isn't acting up. Help!