Versailles electric vehicle vs little train question

There will be a ridiculous wait for the golf carts; the little bus trolley thing runs fairly often and you probably need wait less long for that. But the garden is small and easily and best done on foot. The distance to the Hameau and Trianon at the opposite end of the estate is a lovely walk and I did it last year in my mid 70s. With your time limitations you probably won't have time for all of it, but certainly the chateau and the gardens and for that no transport is needed. I would book a King's apartment tour mid day if possible to avoid the long long long security line and start with the gardens in the morning and then in the late afternoon before you head back. The fountains only run for a short period in the morning and afternoon. If you don't book the King's apartment tour then get there at least half an hour before the Chateau opens to avoid the worst of the security line, but if you do that and visit the Chateau first thing, the fountains will probably not be running when you get to the gardens, so it may not be worth the added expense. You can check schedules for your day; it may vary at different times of the year. Here was our experience with the fountains in October a couple of years ago.https://janettravels.wordpress.com/2016/02/15/fountains-of-versailles-a-little-chaos/
We did the Chateau years ago when it was only moderately crowded and then did the gardens again recently without braving the Chateau crowds.

It can be difficult to get a seat on the train although they really pack people in tight (it’s not very comfortable), you spend time waiting for it to fill up and then leave. When you take it back you have to wait in a long line in the sun.
The golf carts do have a long line but people are returning them often (they are expensive) but you may wait a long time. You cannot reserve one ahead.
The most fun way is by bike, but I hear you that it may not be possible.
I do find it’s a long walk to the two trianons and especially to the hamlet and I’m a walker.
Seeing the two trianons and the hamlet are well worth it whatever way you can.

But the garden is small and easily and best done on foot

Not sure you meant to say the gardens are small, quite the opposite - they are massive. Even the formal gardens with the fountains. But they are best seen on foot.

On fountain days, they do not all run at once (they never did actually). There should be a schedule for which ones at which times, there are hundreds of fountains but the main ones on the chateau axis are the best to see.

It is a very long walk to the Trianons and especially the Hamlet. You may run out of time to see those.

If you can and the weather is nice, bring a picnic lunch to enjoy down by the canal. Better, cheaper and faster than the onsite restaurants.

I got one of the golf carts several years ago when my wife's knees were giving out. It took about an hour in the afternoon waiting in line for my turn for the next returned cart. But it was neat. They have a certain "track" you have to stick to. Stray off and the power is killed and you'll have to push it back to the "track".

Thank you everyone for your replies. Going on a musical fountains day isn't what I was initially planning to do, but that's what worked out best with everything else we want to do. I guess when we are done with the Palace itself we will head out to the gardens and see what the wait for the various things are. If it's short enough to wait, we will, and go to the Trianons. If it's too long we will just explore the garden itself and save the Trianons for a future visit.

If you get to the golf carts when they open you’ll get one right away. Maybe do the palace after the gardens?
The Petit Trianon, the Grand Trianon and the Hameau (hamlet) are the best part imo. I hope you get to see them this trip.

I understand it’s the only day you can go, but we found the “fountain” days were much more crowded than days when the fountains aren’t on. Fwiw, we were not at all impressed with whatever fountain was on, the music they blare on a bad speaker system was really annoying, and twice the normal crowd there for the fountains was a huge drag. Is there any way you can switch days?
Just want you to enjoy your day there (we love Versailles) and trying to offer helpful info.

Looking at Google maps, it appears the walk from the Palace to the Trianons is about 30 minutes. I'm guessing that is walking at a brisk pace, not a sightseeing, meandering route. Does that sound about right for those of you who have been there?

As of right now I am thinking of arriving early (gardens open at 8:00) assuming I can get the rest of the group moving and visiting some of the gardens first thing in the morning. We would then do the 9:30 Kings Apartment tour (which I believe would allow us to use a different, shorter security checkpoint line). After the tour we will see anything else in the Palace we want to fight crowds to see and then head into the gardens for lunch and walk over towards the Trianons. We'll see how far we get before we have to leave at 4:00 to head back to Paris.

30 minutes sounds about right. Its a good mile from where you exit the palace to the gardens. It is downhill, but remember, that means it is uphill going back.

I do see the same on Google Maps but I don’t think it’s very realistic. Maybe walking the most direct route and at a fast pace it’s possible.
I don’t think that’s a good way to enjoy Versailles though.
From the Grand Canal up to the Palace it’s uphill for sure, but I’ve always thought it was flat from the Grand Canal out to the two Trianons and the Hameau.

I'd say 30 minutes at a more leisurely pace. But I tend to walk fast and could easily do it in less. It is slightly uphill on the way back.

We did the walk to the Trianon in about 15 minutes starting at the base of the gardens and walking through the woods from there. We did the gardens in the morning for about half of the fountains and then walked over to the Trianon, did that, and walked to the Hameau and then back to the gardens for the afternoon fountains. It was a long tiring day, but we are also ancient. The Trianon is only open in the afternoon.

janet, do you mean by the Grand Canal? Which Trianon did you visit?
I’m gonna walk it next time... : )
I usually rent a bike but most recently I took the train, and regretted it.