Our experience with summer flights to Europe, at least the ones leaving from Seattle, is that prices only go up as the planes fill. Our best deals were bought 11 months in advance, our worst was trying to play chicken with fares and losing badly.
Her only risk is if her first flight into Seattle is delayed. No point in the terminal is more than 20 minutes away.
While busdriver11 is entitled to her opinion, I have arranged plenty of 3-leg flights to international destinations for my daughter & myself that went well - and we have at times experienced terrible problems with 2-leg or even 1-leg flights. A delay is a delay and can occur at any point in the flight. Luggage can be mishandled or lost at any point. While it is true that having multiple flights increases the chances of that happening, it is a small marginal increase – in the same way that passengers who are frequent flyers have a greater chance of experiencing a mishap than passengers who fly only occasionally. If there is a 5% chance that a given flight will be delayed, then in theory that chance rises to 15% if there are 3 flights. But in practice there are all sorts of other factors that impact those problems – including issues local to the specific airports. (Some airports experience more problems because of the nature of the facilities and local climate— airports that handle a large amount of traffic simply are more prone to delays in takeoff and landing related to air traffic.
I think the only relevance in terms of a multi-leg flight is that a little more leeway should be given with layover time between the 2nd and 3rd leg, than what is needed between the 1st and 2nd. The worst thing that happens if a person misses a flight is that she misses her flight. Usually that means getting rebooked onto the next flight out. While that isn’t a desirable outcome, it is also part of the process of travel and something that any passenger should be prepared to deal with. (As well as the potential for lost luggage – something to consider when deciding what to pack in a carryon).