I'll give you a couple of tips on the California Zephyr. There is a good light rail system from the Denver airport to the newly built Denver train station. Attached to the new train station is a nice new hotel.
The train leaves Denver @ 8:05AM MT (could be late - it comes from Chicago). For your first overnight trip on Amtrak I recommend the Roomette instead of trying to sleep in coach seats. You should be able to get breakfast on board the train unless it is running quite late.
The two most beautiful daytime sections of the route are the Glenwood Canyon east of Glenwood Springs and the Ruby Canyon west of Grand Junction going into Utah. If the train is on schedule (sometimes), the sun will be setting before you get very far into Utah. The train will be stopped for about 20-30 minutes in Salt Lake City for maintenance and refueling in the early morning hours.
The train is scheduled into Reno at 8:23AM PT. The Reno station is below street level. You will be taking an elevator up to street level to get to your rental car.
Instead of going into Yosemite via Lee Vining, go west on US 50 to Placervillle and then south on CA 49 through the gold country to Mariposa.
After your visits to Modesto and Twain Harte, go back through Yosemite to go over the Tioga Pass on the way back to Reno. If you have some extra time going back north on US 395, you can stop in Carson City to see a museum and maybe the home of Mark Twain's brother.
Do not try to get gas inside Yosemite or in Lee Vining. Modesto or Merced would be the best choices. Gas is cheaper in the Carson City/Reno area.

From Reno you do not drive over Donner Pass to get to Truckee which is on the eastern side of the Sierra.

How late in September?

Days 5-6 don't make sense to me unless you stay IN Yosemite Valley. Keep in mind that mountain road repairs are done in the summer and fall months, so there can be traffic delays.

September is the very worst of our fire season so you'll have to keep abreast of conditions and make changes at the last minute if necessary.

Staying in Mariposa for Yosemite makes no sense -- and if you DO end up driving Lee Vining into Yosemite Valley and on to Mariposa, that is a crazy day. I would not even bother going to Yosemite unless you stay 2 nights IN Yosemite Valley or in nearby El Portal. By the time you drove through the back country and got to the Valley you wouldn't have much/any time for Yosemite Valley itself.

>>May seems to early,<<

It would be too early (most likely) to drive over Tioga Pass since it is often closed until late May or Early June. HOWEVER - there is absolutely no better month to visit Yosemite Valley and the Gold Rush foothills. The Waterfalls in YNP would be at their fullest (in Sept/Oct they are essentially dry) and the foothills would be green and gorgeous (dry and brown in Sept/Oct)

I never got the chance to see the old Union station in Denver. It is now like a food court with several restaurants and a book store with the Crawford hotel upstairs.
I did figure out how to save about $200 on your train trip. (I've done it myself). Instead of having the Roomette all the way from Denver to Reno - about $754, Take the coach seats from Denver to Salt Lake City.
The train, when on time is in SLC about 11PM and leaves at 11:30PM. Book a Roomette on the same train from SLC to RNO (about 10 hours). The combined fares are about $546. You would pay for your 2 or 3 meals on the train or you could bring some food from Denver if you wanted to.
To save money when traveling with my wife west from Chicago, we took coach as far as Omaha NE and then transferred at 11PM CT to a Roomette as far as Glenwood Springs.
The hotel attached to the new Union station in Denver is the Oxford. When coming into Union Station the train backs into the station past Coors Field.
If there are no available rooms in your price range inside Yosemite, there are cabins that have a shared bathroom at the BUG hostel near Midpines. Otherwise, stay in a hotel in El Portal.
I also encourage you to get enrolled in Amtrak Guest Rewards (free) to earn points toward future trips on Amtrak. In February my wife and I will be making a trip from Chemult Oregon to Tucson and return. Two sections of our trip will be in coach using AGR points. I also earn some AGR points every time a rent a car (usually from Enterprise).

I would echo Janis - if May is a possibility, grab it with both hands. The waterfalls in Yosemite will be full (as opposed to trickles or even dry in September,) the risk of fires will be low, and the Gold Rush country along CA 49 will be fantastic - flowers, rushing rivers, historic and lovely old towns... best time of the year.

50 and 88 are maintained year round. 108 is seasonal and opened on May 30th this year.

If you follow the advice I gave about switching to the roomette at SLC, you should stay on the train all the way to Sacramento. The trip up (and down) over the Sierras between Reno and Sacramento is great.
The train nearly always arrives in Sacramento before 3PM. I have rented cars several times at the Enterprise in Sacramento.
You can visit south Lake Tahoe before or after Yosemite and the gold country along CA Rt. 49.
I'm hoping that you had a great Christmas

I would stick to September. Yes, the waterfalls will be dripping, but in May you'd almost certainly miss the Tioga Pass and probably also Glacier Point, a not-to-be-missed view.. For me, the Yosemite high country is awesome.

I agree EXCEPT if we have a bad fire year the trip could be a total wash out. Not just Yosemite but even Tahoe and the foothills. The Waterfalls in the Valley are worth missing Tioga IMO . . . plus they have very little time so really a couple of days/nights in YNP is all they have time for.

Even if a fire isn't threatening YNP directly, the smoke and haze would ruin any views. Unfortunately we won't know the fire situation until the time. One thing -- fires aren't likely in May.

September can be a total bust if there is fire, including the access roads being closed, bad visibility, and bad air quality.

2018 was a disaster!

No one here can predict the weather, although at this point it's quite a big snow year. That means that Tioga Pass, Glacier, etc will likely not be available in May.

October can also be a nice month, too.

I would just pick the month that looks best for the rest of your itinerary. I would also ignore much of the advice about "you can't do this or you shouldn do that" and stay flexible. As of now, who knows what will be open next year, when, and what will be damaged or closed.

People sometiimes do just get up very early and drive in for a day or stay just one night.You probably will be getting up early anyways since traffic will be ridiculous both in early (waterfall) season and throughout the year if they are doing road construction, or if there have been landslides that have closed off any of the access roads from the Central Valley. One thing to be said for going later in the year is that it is usually easier to get in via the beautiful Tioga Pass Road, and scenery along the Eastern Sierra via 395 is spectacular.

My revised itinerary. We have decided to go in May in hopes of avoiding wildfires.

1. Fly to Denver, night in Denver *
2. Board Zephyr to Sacramento, night on train
3. Sacramento, rent car drive to Modesto, night in Modesto (arrive at 2:15, rent car & drive to Modesto (75 miles)*
4. tour Modesto & drive to Yosemite, night in El Portal (105 miles)
5. Tour Yosemite, night in El Portal or Sonoma (50 miles)
6. Drive to Twain Harte, Strawbwrry, Dodge Ridge, (35 miles) Drive Sonoma pass to Carson City * (75 miles from Dodge Ridge)
7. Tour Carson City, tour Virginia City, night in Reno * (50 miles)
8. Drive to South Lake Tahoe (60 miles), 10:00 pm flight home

Absolutely NO reason to stay in Modesto (of all places!) The drive from sacramento to Yosemite is not long enough to have to stop over anywhere. Or if you just want a night somewhere - stay in the (scenic) foothills - not in the decidedly un-scenic Modesto. PLEASE don't stay in Modesto - a second night in sacramento would make more sense than that.