Let's take the historiography of Indo-European Studies as a means to understand the way(s) the comparative method and internal reconstruction interact.
Originally, at the beginning of the 19th century, people more or less equated PIE with Old Indian. Then people realized that the vocalism of Old Indian short a / long A could not be the original situation, because there is no reasonable way the system with a/A could possibly become Greek a/e/o vowels.
Besides, there also are a number of phenomena known as the Law of palatals and Brugman's Law, which confirm that the original situation must have been that of Greek, not that of Old Indian.
This led in the 1870-1880s to a new model, Neogrammarian PIE.
At the same time, Saussure showed that the introduction of "coefficients" could simplify and rationalize the morphology of apparently odd vocalic alternations.
These "coefficients" were quickly understood as weakly articulated consonants of laryngeal nature.
Hittite provided the final impulse for the emergence of Laryngeal PIE.
Neogrammarian PIE is a kind of empirical vowel-oriented model of PIE.
Laryngeal PIE is rather an algebraic structuralist model of PIE.
Maybe you should read some Indo-Europeanist literature, like Fortson IV's book.
Hope this addresses your numerous questions about this topic.
