I hadn't heard before "half-life" nor "parent-daughter" for nuclides widely separated on a decay chain, but I don't know everything neither.
What is clear is that the first disintegration, from 238
U, is the slowest by far, so the subsequent ones influence very little the pace at which 238
U disappears. Since 206
Pb is the only end product, it's also the pace at which it's created.
The chain is detailed there, especially in a diagramhttps://en.wikipedia.org/wiki/Decay_chain#Uranium_serieshttps://upload.wikimedia.org/wikipedia/commons/4/4e/Uranium_series.gif
Your explanation with 50%, 75% and 25%... is correct.
If computing the products in small amounts after a short time, starting from purified 238
U, the disintegrations with shorter decay times would have an influence too. The half-life from 234
U to 230
Th is a quarter million years, so one year after purifying 238
U, the amount of 230
Th would be limited not only by the decay from 238
U but also from 234
By the way, detectors of ionizing rays catch essentially single particles, so they are damn sensitive, and as they distinguish the energy carried by gamma rays, they can also pick very low proportions of one radioactive nuclide among other ones. So together with mass spectroscopes, they can detect traces of a nuclide that would be impractical by most other means. Then the proportions of very rare nuclides in a decay chain can be significant. Very rare nuclides, and the ability to measure their proportion, makes also dating possible.
If comparing the rays emitted by nuclides in a chain, rather than the proportions of the nuclides, nuclides with a shorter live, which disappear quickly hence are rare, are also more radioactive - this cancels out: at "equilibrium" composition in a chain, as many disintegrations create and destroy an intermediate nuclide.