Trying to determine trail ticket options...

Do you know if the Germany Rail Pass can be used on the S-Bahn?

The S-Bahn is a train of the Bahn, so the GRP can be used on it. Not so for the U-Bahn, trams, and buses in metro districts (Verkehrsverbünde).

It will probably be less expensive to purchase Berlin to Köln as Sparpreis tickets, Köln to Münster as Länder-Tickets, and Munich to Dachau as a local, MVV, ticket.

For Berlin to Köln, you need only tickets for three adults. The 14 yo, if declared on the ticket, is free.

For Berlin to Koeln and Koeln to Muenster, just go to the Bahn website, and put in your travel dates and four passengers with the ages. Remember that "hbf" is hauptbahnof, the main train station in a city. Also remember that the search defaults to the current date and time, so make sure to change it to your desired date and time of travel.

https://www.bahn.com/en/view/index.shtml

You will see Savings Price fares and Flexprice fares. If you can accept the restrictions on Savings Price fares, you can save a fortune. If you need full flexibility (or just buy on the day of travel), you will pay the higher Flexprice fares.

For instance, for your Berlin to Koeln trip, on the randomly chosen date of August 23, 2018, for 3 adults and one 14 year old (your 17 year old seems to be adult priced), I get €366 for Flexprice and €161.70 for Savings Price - for all four of you.

Now, once you've gotten the prices for your trips, then compare these prices with the German Rail pass options you are looking at. Remember that the pass gives you full flexibility, so while it will be more expensive than the Savings Price tickets, it may work better for your needs because it may (or may not) be cheaper than Flexprice tickets.

The Munich to Dachau ticket is part of the Munich transit network and is cheap; don't use a pass day for just this one trip. Sure, if you have a pass anyway, it's covered, but don't include this in your pass calculations.

At most, you have 4 days, Berlin to Köln, Köln to Münster, Münster to Köln, and the day trip to Dachau.

The round trip to Dachau, S-Bahn plus bus, can be done for 16.10€, far less than a 4th day of rail passes for all 4, so don't get a 4th day.

Two 3 day youth passes and an adult twin pass for 3 days would cost $878 (753€ at todays conversion).

All four of you can have unlimited travel for a day between Köln and Münster for 45€ with a Schöner Tag Ticket. If you make the trip in two days, that's 90€ (in one day, it's only 45€).

Assuming you do the Köln-Münster trip in two days, that leaves 688€ for the Berlin-Köln trip. Even fully flexible, full fare tickets from Berlin to Köln are only 366€.

You're saving $375 with no loss of flexibility. With a Sparpreis ticket, you'll be committed to a specific train, but save even more.

Seems like a no brainer.

This begs the question, how are you getting between either Cologne or Berlin and Munich?

All four of you can have unlimited travel for a day between Köln and
Münster for 45€ with a Schöner Tag Ticket. If you make the trip in two
days, that's 90€ (in one day, it's only 45€).

The STT is only valid on regional transport (RE, RB, ERB, ... and bus/tram/u-bahn/s-bahn) and not on IC or ICE. The difference in time between these two for Köln-Münster however isnt that big. Using the direct IC, it can be done in a little under two hours (1:45). Using the direct RE train, it takes two hours.

The S-Bahn is a train of the Bahn

Not all S-bahns are operated by DB. A small number are run by other companies like Abellio and Regiobahn.

A small number are run by other companies like Abellio and Regiobahn.

Do those other companies accept the GRP?

Looks like Abellio and Regiobahn are private companies operating trains on the Bahn owned rails under the Bahn's privatization (profitization) policy. They are like Mittlerheinbahn, Meridian, or ALEX for regional trains. The Bahn is their Aufgabentrager (administrative authority?). They run on the Bahn's schedule and accept the fares set by the Bahn.

The U-Bahn(en) are actually run by companies under the auspices of the local Verkehrsverbund. They do not accept the GRP.

I know of one really independent rail company, BOB (Bayerische Oberlandbahn), which runs their own trains on their own tracks in a network based at Holzkirchen south of Munich. They run trains to Munich (on Bahn tracks), Tergernsee, Lenggries, and Bayrischzell. Last I knew, they don't accept the German Rail Pass (but they do accept Bayern-Tickets).

On the German Rail Pass, the Twin price is cheaper than the Youth price. So as long as the family is sticking together, you would choose two sets of Twin passes and ages won't matter.

@Lee

The companies mentioned by you (and many others) are not subsidiaries of the DB and do not operate on behalf of the DB. Regional train traffic is publicly advertised by the respective federal states (usually for 10 years) and those companies have won the contract, in all cases against the competition of the DB. They are simply offering more value for money.

All that has nothing to do with the question of which pass on networks operated by non-DB companies is valid. The answer is simple: every operator on a public network has to be a member of Tariff Association of the federal and non-federal railways in Germany (TBNE) and must honor every valid rail ticket. There are very few exceptions such as the both Bavarian cog railways, Zugspitzbahn and Wendelsteinbahn, which do not run on a public network.

BTW, the BOB does not have a network of its own. The tracks belong to the DB Netz AG (which is legally separated from the DB), with the exception of the line from Schaftlach to Tegernsee, which belongs to the private Tegernseebahn.