what difference would this make

It looks like the OP is aware of the EU visa rule where Americans have up to 90 days within six months visa-free.

I have dual citizenship, US and Netherlands, so this is of no concern. Those are just the dates I need to travel to AMS, and also again in September, so I'm just trying to make it economical.

For the record, these will be J tickets.

I just want to make sure this will not backfire in any shape or form.

Part of the fare rules for the first flight (April 8 to June 25) say the following:

COMBINABILITY

DOUBLE OPEN JAWS NOT PERMITTED. END-ON-END NOT PERMITTED. SIDE TRIPS NOT PERMITTED APPLICABLE ADD-ON CONSTRUCTION IS ADDRESSED IN MISCELLANEOUS PROVISIONS

Is that what I have to worry about?

No. Those are fare construction rules. They are inapplicable to this scenario. You don't have to worry about anything.

Nested tickets do not violate the CoC. As LBJ explained, there may be an issue where you use them to evade a fare rule, the classic example being the Saturday night stay requirement (which is now often framed as a Sunday night stay requirement). None of that applies to this scenario.

Thanks everyone for the re-assurance. Not only did it save my a few grand, it also meant that the flight I wanted was much more reasonable. Just booked all the flights and hope not to report back with a "whoops, that didn't work" message.

The fare combinability rules in the fare rules limit how you can combine fares onto a single ticket. It doesn't limit what you can do when buying the fares on separate tickets. The limits on ticketing practices involving multiple tickets is not in the fare rules, it's found in the Contract of Carriage. There are various forms of nesting you can do with multiple tickets and many of those are not prohibited by the CoC. For example, I can buy a roundtrip from DTW to NYC and nest a separate roundtrip ticket from NYC to Europe within that to get a cheaper price without violating the CoC. The fare rules will likely prevent me from combining these fares onto a single ticket, but the CoC does not prohibit buying them as separate tickets. It's only the specific case of using nesting to get around the minimum stay requirements of the cheaper fares that is prohibited. Your out-and-back trips to AMS involve Saturday night stays, so you aren't defeating the fare provisions of the cheaper US-EU fares which require that. Therefore, it's not a CoC violation. Try pricing a Sun-Fri AMS trip vs. a Tue-Tue trip and you will see the massive difference in fares.

Taken at face value, OP is not evading a fare rule. Rather, OP Is taking advantage of POS faring which is perfectly fine.

I've done this on Delta. No need for two different airlines. It's legal.
I also did it to Europe, JFK to Dublin

The big problem for me was simply that when my plans changed I was doubly screwed.

ALSO, the airline wants to know you have a Visa, the length of that visa is a different story. When asked about my length of stay, I gave them the dates I was leaving, in the OP's case, the following week.
I also had one way tickets to Europe because I was leaving on a boat. During check-in, they would ask when and how I was departing and I would tell them and most of the time, the ticket agent would still ask supervisor, but it was never a problem, not once.

Yo should never travel with a passport that expires soon (within 6 months), but having said that, they could not deny boarding if OP has second ticket returning in a week.

Question about end-on end fare combinations
 

II have booked travel on two separate reservations and fear that I may have violated a prohibition on end-on-end combinations. I am hoping those of you who have a good grasp of fare rules can help. Apologies for the lengthy post but I want to provide sufficient detail.

I took advantage of a recent TATL promotional fare for flights between select cities to book JFK-CDG-JFK, leaving 01/18. For positioning, I also booked, on a separate PNR, xxx-JFK-xxx, where xxx is my Northeastern US home airport. Tickets were purchased on Delta.com.

Flight 1: xxx-JFK (Ticket B)
Flight 2: DL 262 JFK-CDG (Ticket A) departing 4 hours 50 minutes after arrival at JFK
Flight 3: DL 263 CDG-JFK (Ticket A)
Flight 4: JFK-xxx (Ticket B) overnight in NYC, departing the day after arrival from CDG

Do I have an end-on-end combination of flights? Flights 3-4 cannot be booked as a legal connection but flights 1-2 could be.

The fare rules for Ticket A: JFK-CDG-JFK, do not permit end-on-end combinations (fare basis code VQ2X86M3). The fare rules for Ticket B: xxx-JFK-xxx (fare basis code UA7UA0MJ) are less restrictive and permit some end-on-end combinations, but not my international route.

If there is a problem, I want to deal with it now and not take any risks, so I called the Medallion line. The agent was unfamiliar with the term end-on-end, but said she would contact a supervisor, putting me on hold. When she returned, she advised that the “reissues department” examined my specific fights and said there was no problem with the combination. I still feel uncomfortable and am turning to knowledgeable members of the FT community for either assurance that all is good or suggestions regarding what I might do to. (FYI, I am not interested in tricks or subterfuge, just practical above-board suggestions.)

Thanks.

What you've booked is an end-on-end combination (i.e. a round trip within a round trip in which the flight coupons are used in the proper sequence). Airlines generally allow end-on-end combinations, though many restrict such combinations with low fares.

Did you break the fare rules?
Yes. Your fare prohibits end-on-end combinability and you booked separate tickets with the intent to circumvent the fare rules.

Is there a risk that Delta will cancel your tickets?
Virtually none. Airlines are too busy to strictly police fare rules, especially minor fare rules like combinability. The only issue that airlines seem to care about enough to crack down on are hidden city ticketing.

What are the risks of what you've booked?

• Delta could refuse to re-accommodate you in the event that one trip is delayed, impacting the other trip. They probably would help you in this situation, but they don't have to. Given your long layover on the outbound and overnight stay on the return, I don't think this is too much of a concern. In addition, in the event of severe weather issues, your options to rebook (i.e. through a different connecting point) may be limited.
• There's a possibility that you could fly to JFK without your passport since they won't check upon check-in / boarding for your domestic flight.
• You likely will be able to check your bag through to your final destination on the outbound trip, but you will need to specify this at check-in and your bag allowance for your international segments will not apply for your domestic flights (though you may get a free checked bag via status).

The above is incorrect. End-on-end fare restrictions have to do with combining certain fares on a single ticket. In order to combine fares on the same ticket in such cases, you will typically need to upfare to a higher fare class that does not have the restrictions. There are no ticketing or fare rules violations if you simply book the cheaper fares on separate tickets. By the way, what you acutally have is a side-trip which is probably the fare combination restriction that is preventing the combination. This is the typical language that restricts this in the fare rules --
END-ON-END MUST BE AN A-B-A COMBINATION. SIDE TRIPS NOT PERMITTED.

You are perhaps confusing these with back to back ticketing which is booking multiple tickets to meet the minimum stay requirements (typically a Saturday night) of the cheaper roundtrip fares but with no intent to meet the minimum stay requirements of the fares. This generally involves booking a roundtrip in the reverse direction and nesting it within another roundtrip fare. This is a prohibited ticketing practice. But this is not what you are doing here so your bookings are perfectly acceptable. While you are nesting fares, you are not doing it to subvert any minimum stay requirements in the fares, so there is nothing wrong with it at all. The main issue is that you are not as well protected in the event of schedule changes or IRROP's.