As someone who generally prefers public transit to driving (especially in a foreign country - a lot will depend on
where you're traveling. I usually travel solo but think in general it would scale pretty well. Of course if your kids are poorly behaved then it'll be more of a challenge.
I think having some familiarity with the infrastructure can go a long way into making the trip easier. Knowing where platforms are, which stations are easier to transfer at, etc.
2 – Don't forget road tolls, parking, and surprise maintenance.
3 – The most consistent "pain point" I've seen with transferring is simply walking from platform to platform. I can only think of a handful of stations that I'd actually consider difficult (e.g. BART's Millbrae and Madrid's Atocha station).
4 – Again, parking. In most big cities you're not going to roll right up to your destination and park.
5 – My experience has been it's as difficult as you make it. Hell I saw someone bring a refrigerator on Muni. Some places like Japan have low cost courier services that entirely negate the need to bring luggage with you. Just drop it off with the courier at the airport and have it sent to the hotel or nearest 7-11. In other places you'll find luggage racks or areas on the trains. Alternatively, pack less stuff. If you're traveling by car and need to use a rooftop box don't forget the hefty fuel consumption penalty.