Personally, I think most of Charlie's actions in regards to Bella in the saga can be interpreted as him not wanting to lose his only child. I think if you consider that as his motivation, most of his actions make sense.
Begin Twilight Saga from Charlie's POV:
We don't know what went on in the divorce, for all we know he could have been fighting hard to get more access to Bella and lost the fight. Then he has to deal with the fact that his daughter is being raised by a woman who hates his home town and is not quiet about that fact, something that his daughter picks up on. So now when he does get to spend time with his daughter, she's upset because she doesn't want to be there with him. Eventually this leads to his daughter refusing to visit him all together, instead insisting that they vacation somewhere that she likes, which further limits the time he can spend with her. My personal opinion is that Renee was feeding Bella's dislike of Forks and giving her a degree of support in her bad attitude towards the place and, by extension, towards her father.
There isn't much that Charlie can do about any of this because his ex-wife has primary custody and if he presses the issue he risks losing what little he does have. Just getting a new job closer to where Renee and Bella lives may or may not be an option, while I'm certain Charlie is a very good cop I would also think that police departments in larger cities like Phoenix wouldn't be falling over themselves to hire someone from a small town where he doesn't see much action.
Now, fast forward to slightly before Twilight begins, Charlie gets told that his daughter, the daughter who he only sees two weeks a year and who has made it no secret that she hates the place he lives, announces that she wants to live with him. He loves his daughter and is thrilled by the apparent 180 degree turn she is making in her attitude towards being around him. However, they do not formally change the custody order, this means that Renee still has primary custody, which means that Renee can end this situation whenever she likes.
So, Bella arrives in Forks and doesn't seem thrilled about being there even though the move was her choice. Charlie doesn't have experience with his daughter and tries to do things that will make her happy there, like buying her a car and encouraging her to make friends and be involved in activities (like the school dance). She is sort of going along with all of this and then she announces that she has a boyfriend, after saying that she isn't interested in any of the boys in town. Charlie likes the boy's father well enough and the young man appears polite and respectful. Then later that evening Bella leaves, saying that she can't get stuck in Forks. She is seriously injured a few days later in a horrible accident, but when she comes to, she still wants to live with Charlie, apparently in part because her boyfriend and his father flew down to talk with her. Charlie forgives her and is happy to have her return with him. Her boyfriend's sister turns out to be a wonderful young woman who is thrilled to assist Bella during her long recovery and Bella seems to be enjoying living in Forks, largely due to her relationship with Edward and her friendship with Alice.
Then Bella turns 18. This means that Bella is legally an adult and the custody ruling is no longer in force. Legally, Bella can chose where she wants to live and does not even have to live with either of her parents. Alice and Edward appear excited about Bella's birthday and throw her a party. A few days later, Edward breaks up with Bella and leaves. Bella spends a week in a nearly catatonic state and Charlie is willing to bring in Renee in hopes that living with Renee again will help Bella heal. When they start packing, Bella throws a fit and insists that she is staying in Forks. Charlie doesn't want his daughter to move and accepts this. The next several months, Bella acts like an automatron, my guess is that at the beginning Charlie was trying to convince himself that she was improving (it was certainly an improvement over the first week). He probably should have said something sooner, but he isn't perfect and he could also have been worried that his interference might make her worse.
Skip forward to when Alice shows up. Charlie is happy to see Alice, but admits that he is concerned about what her presence will do to Bella after she leaves. Bella then runs off. Charlie doesn't know where she is for three days. When she comes back, he is not nice to Edward. He makes it clear that Edward is not welcome in his home ever again. Then, the first time that he really gets to talk to Bella she informs him that she is staying in Forks but will move out of his house if he doesn't permit Edward to visit, the unspoken indication is that if she does move out she will be moving in with her boyfriend's family. Charlie likes that idea even less than he likes the idea of having Edward in his home and relents. He does however ground her and sets rules about when the boyfriend can and cannot be in the house. Bella accepts these restrictions fairly well and Edward comes over every day. Charlie makes certain the boy knows he is persona non grata as far as Charlie is concerned and then comes up with a plan to (hopefully) decrease Edward's influence by ungrounding Bella on the condition she spend time with people who are not Edward Cullen, specifically encouraging her to spend time with the young man whom Charlie thinks would be a much better boyfriend for his daughter.
Edward still keeps coming around. Then the two of them announce their engagement. Charlie is opposed but relieved that his daughter is not pregnant and them getting married is better than them living together, Charlie can hope that marriage will make it more difficult for Edward to leave Bella again. He knows that Renee doesn't approve of young marriages and hopes that she will throw a fit over this one.
The wedding is lovely and then the newly weds come back from the honeymoon with the news that Bella has contracted a rare disease. Bella sounds really bad on the phone and her doctor father-in-law won't let him see her. If Charlie did come by the Cullens's house, I am certain that he would have gotten a full does of resignation that he couldn't see his daughter, courtesy of Jasper, not to mention that Carlisle would probably be getting information from Alice and Edward.
Jacob comes by the house and lets him know that Bella is no longer sick and things are "weird but good." Charlie wants to go see Bella immediately but Jacob stops him, and then strips and turns into a wolf. Charlie is in shock. Jacob turns back into a human and informs him that the world is a much weirder place than he thought it was. Charlie sorts this out and becomes suspicious concerning his daughter's rare disease. Jacob informs him that Bella was sick and part of her cure has altered her physical appearance. Charlie also discovers that his daughter has known that there was something supernaturally odd about her in-laws ever since she first came to Forks. Charlie rants for a while on that but once he calms down, what he wants is to visit his daughter and to not be told too much about the supernatural stuff. Jacob also informs him that if he can't accept the situation and the changes in his daughter, Bella and the rest of the Cullenses will disappear, making it unlikely that he will ever see his daughter again.
So at the visit Charlie accepts the changes, accepts that his daughter has produced a child in an impossibly short period of time, and accepts that he has to just deal with all of this because if he doesn't he will lose his daughter and his granddaughter forever.
End Charlie's POV
Also to continue this very long post, when you add in all the stuff that Charlie doesn't know about like Edward sneaking into the house at night undetected, wanting to consume Bella's blood, other vampires wanting to eat Bella. The whole Twilight series could be considered a father's nightmare.