Honestly, you have that amount of luggage, take a cab or some sort of airport bus that is setup for people with luggage. Yeah, that family was obnoxious (or at least clueless) but crowded subways and commuter-type trains aren't intended for people with more than light carryons at most. (And even those can be a pain during rush hour.)
That was definitely one of those cases of where that family shouldn't have used the CTA. They should have used a taxi. It was a family of 5.
For the people not in the know:
I was sitting on the far top right single seat. They were sitting in the first 2 vertical oriented row seats nearest to the door there.