Travel from Ortisei to Seefeld on a Saturday in Sept without a car

You should be able to get there in less than 4 hours.

Bus 351 from Piazza San Antonio Ortisei dep 7:34 am to Klausen arr 8:18 am.
Train 100 from Klausen dep 8:25 am to Brenner arr 9:22 am
Train S-3 from Brenner dep 9:33 am to Innsbruck Hbf arr 10:13 am
Train S-6 from Innsbruck Hbf dep 10:38 am to Seefeld (Tirol) arr 11:14 am

That is the first departure in the morning, there are others.
Specific date in September is important as there is some construction workk on the rail lines in August to early September and some trains may have replacement buses between Klausen and Innsbruck.

Ok yes, we are traveling on a Saturday in Sept. I hope that isn't a problem.

What day in September?

Sept 16th. Thanks so much for your quick responses

Then you look good for that schedule.

Do I need to worry about the tight departure times? If not, when would you suggest buying tickets? Does the Val Gardena Mobil Card we will receive from our Ortisei cover part of this trip?

I don't know the extent of that card. The cost of the transport from Ortisei to Innsbruck Hbf is 22.40 EUR per person. Tickets from https://www.suedtirolmobil.info/en.
Ticket for Innsbruck Hbf to Seefeld is 4.30 EUR per person. Tickets from https://www.oebb.at/en/

There is no reason to buy them until you get to Ortisei, as nothing requires a reservation, a ticket is good for the day an there is no discount for advance purchase. You can also buy the Seefeld tickets at Innsbruck Hbf as you have almost 30 minutes there.

The other connections are designed connections. The bus from Ortisei drops you at Klausen station and you board the train to Brenner 7 minutes later. At Brenner, the S-Bahn to Innsbruck should be waiting for you at the station so you just get off of one train and onto another. It is all included in a single ticket. You just need a ticket for the final leg to Seefeld.

If you miss a train, you just wait for the next one. At most, you have to wait another hour..

That is perfect! I appreciate your time and expertise! Thank you so much!

I do have a few more questions on this trip.
The trains from klausen to Brenner then to Innsbruck.
Do we buy these tickets online via trenitalia the day of departure?
Do we need to validate our ticket once we get to the train station at Klausen and then again in Brenner?
If we happen to miss one of the trains, is the ticket still good for other trains to the same destination?
Thank you so much

You can buy these tickets, along with the bus from Ortisei to Klausen from Suedtirol Mobil as it is all part of the regional transport network.

Thanks again for all your help!