This started as a comment on Mophotla but it expanded so much it needs be an answer.
First, the two bookings trick is a great trick.
To expand on the three bookings booking process: search with whatever engine you prefer but book with the airlines directly. I checked Air France, British Airways, Air Canada and all of them offer seats after booking any time before check in for a fee. I heartily recommend subscribing to Expertflyer — for five dollars a month you can look at the seat map before booking:
The results look like this.
As a footnote, towards Budapest I found it much, much better to have a short flight first in North America then the long one. Waiting hours in the morning in Europe after the overnight transatlantic flight is brutal. I absolutely refuse to do this and check into a hotel instead if my routing is such.
You could proceed in two different ways:
The advantage of the second method is that you can ensure your daughter and you will be sitting next to each other, since you are booking the tickets for both of you in the same step.
However, it might be worth comparing prices between the two methods, because in general trips originating in Dallas are not necessarily equally priced to trips originating in Budapest, so you might end up saving money with the first method.
If you do decide to make three bookings, book your daughter’s and your ticket directly consecutively to ensure you get the seats that you want.
The best way I’ve found to make this kind of booking is either:
The travel agent option is probably a lot less headache than talking to an airline booking agent directly.
Credit:stackoverflow.com‘