hi i'm not the first person to tell you this (obviously) but you are very wrong. i wrote on a whiteboard and graded your post:
transcribed below for clarity/accessibility:
on your point about house "really trying" to change:
the whole lesson of s7 is that house wasn't "trying to change". that's why so many people criticize cuddy for saying she "didn't want him to change" (7x01) and then breaking up with him. he actually notably becomes a worse partner as the season goes on. house was trying to stay sober, i'll give you that. but that's upkeep from his development in s6, which is what led cuddy to finally get with him (6x21/7x01).
to say that he was trying to change in any other regard is just factually untrue. he brags to his coworkers about their relationship when she asks him not to (7x02), he tries to abandon her child when asked to babysit (a notable downgrade from him offering to babysit in 6x06) (7x05), he lies to cuddy repeatedly after she asks him not to (7x06), drugs her mother without cuddy's knowledge or consent (7x08) (and fakes having plans with wilson to get out of spending time with her twice in the same episode), instead of apologizing for lying to her, he digs up decades old information to pull a "gotcha" (7x09), he doesn't help cuddy out when she asks him to, making her (already hard and stressful) life harder, when a decent partner should be doing the opposite (7x13), completely skips out on an event he'd promised cuddy he'd go to so that he can wallow in self-pity, and doubly blames her for making him a "worse doctor" (7x14), and, of course, completely avoids her when she believes she is dying of cancer, only being able to show up in the final hour when numbed by drugs (7x15).
on your point about house "trying to quit"
he can't both be "trying to quit" (which is untrue, he had been sober for almost two years) and also take vicodin as a passing thought; those are contradicting points. clearly it wasn't a passing thought because it took him multiple days of not seeing her to finally take them. if it were a passing thought, he would've taken them immediately, no?
also this implies that cuddy's anger is only at the act of taking pills, which, is said directly in that episode to have not been the reason.
on your point about house's "ups and downs"
change isn't a quick process, but house had been sober almost 2 years. he wasn't getting sober because of the relationship, the relationship happened after he had gotten sober. yes, sobriety is not an easy or smooth process but the act of taking pills is not the reason cuddy broke up with him, it was, as she directly states, what the pills mean (ie that he can't/won't be there for her, as shown throughout 7x15). cuddy says in 6x21 that it's his choice if he wants to take vicodin again, so clearly cuddy's problem has never lied within his addiction. also, their relationship was almost a year long, and cuddy sat through all of the aforementioned terrible partnership; they had more than enough ups and downs. you phrase this as if this was, like, a month in.
(additionally your phrasing -- "the cancer thing" -- does something a lot of takes on this episode tend to do, which is minimize the effect of the cancer scare on cuddy while treating house's reaction as fair. this is misogynistic; a man suffering because a woman he cares about is suffering should not be more moving or important to you than the woman suffering.)
insufficient evidence, contradictory points, and a clear misunderstanding of the text. see me after class.