help with train from Frankfurt to Nurnberg

Since you specified 4 tickets, you are getting the correct price of 86 EUR, 29 EUR for the first person and 19 EUR for each additional person traveling with you. Your daughter is looking at a price for one person and is getting a 29 EUR price.

HOWEVER, since you are arriving on an airplane, and have no idea if it will not be delayed, NOR that you will get through immigration quickly (there could be a big back-up if several big jets arrive at the same time), you are taking a risk of losing your 86 EUR if you miss the train, and then have to buy full fare tickets for 240 EUR to get the next train 1 hour later. It is a chance I would probably take, but you need to be aware of it. You could also choose to book the 10:35 train and give yourselves some extra cushion.

An alternative would be to use only regional trains, making two connections along the way, and taking an extra 1 1/2 hours to get to Nuremberg. You can buy that ticket when you arrive at the airport Regionalbahnhof (fast trains go from the Fernbahnhof next door). It is called a Quer durchs Land ticket and it is priced at 44 EUR for the first person and 8 EUR for each additional person, so it would cost 68 EUR. Then you would be fully flexible and ride any regional train that gets you to Nuremberg. You can buy it from a ticket machine or spend another 2 EUR and buy it at the ticket window.

So it is 2 hours and 42 minutes on the fast direct train, or 4 hours and 17 minutes with regional trains changing at Frankfurt Hauptbahnhof and Wuerzburg.

I took a direct train from Frankfurt airport to Nurnberg, very easy and fast. I might go for a later train, given the unpredictability of getting through baggage claim, etc.

Sam- Thanks for clarifying the price difference for me. I do see now that I had already selected the 4 adults instead of the 1 adult option. I will talk with the others traveling with me to see how they feel about the slower/less expensive train vs. the high speed train.

Zoe- Thank you for your reply, too! I will definitely consider a later train.

you are taking a risk of losing your 86 EUR if you miss the train, and
then have to buy full fare tickets for 240 EUR

Unless they've changed something since I last read the ABG, if you miss the assigned train on a Savings Fare ticket, you do not lose the entire 86€. You can pay a penalty of 19€ and apply the remainder to a voucher for use only on a later train on the same route that day. So it a trade-off between 240€ up front for a full fare ticket to start with vs 68€ most of the time or 259€ if the flight is too late. [I can no longer find that paragraph in the AGB. I don't know if it's been changed or I only dreamed that part.]

I should also add that I have used the FRA Fernbahnhof many times and it's never taken me more than an hour to go through immigration, get to the Fernbahnhof, buy a ticket, and get to the platform for my train. That's with a carryon so no time at baggage claim, but you'll have two hours. However, I've twice been an hour late arriving in Frankfurt on a trans-Atlantic flight. If you add an extra hour of cushion (ticket the 10:34 ICE) you'd only get to Nürnberg ½ earlier than by regional train. You might as well use the risk-less regional ticket.

I am just going by this page, "Exchanges/Refunds" at the bottom of the page:
https://www.bahn.com/en/view/offers/germany/saver-fare.shtml?dbkanal_007=L04_S02_D002_KIN0060_ST-SPARPREIS_LZ01

Of course, the German Language conditions of carriage govern. This English Language statement is a bit ambiguous:

Exchanges/refunds:
Before the 1st day of validity: possible for a fee of EUR 19.00
After the 1st. day of validity: not possible
Further information can be found on the Passenger Rights page.

What about on the day of validity?

SLA019 has told me that the day-of-travel-exchange has been eliminated as of last December (maybe too many people like me figured how to play the odds.