I don't think the succession line is a problem at all even with a 65-year-old father of two eight-year-old legitimate children born within his marriage to his wife, Princess Charlene. Not to mention if something happened to Albert, his older sister Caroline will step in and help Charlene and her nephews until they are both adult and trained to assume responsibilities.
I'm sure Caroline would be helpful, but the law makes Charlene the regent if something happens to Albert before Jacques turns 18. Given what we know of Charlene's situation, I doubt that she would be capable of -- or willing to -- assume the role of head of state. Remember, the reigning prince in Monaco is a highly political, hands-on job, not a ceremonial head of state.
Princess Caroline is a force of nature in terms of protecting the family and her brother Albert and his wife and their children. I don't recall seen her in articles in relation to Jazmin or Alexandre like she's with all the extended Grimaldi clans of cousins, nieces, nephews, grandkids, etc.
I think you're projecting into what Caroline's attitudes are. Over the years we've seen reports about a lot tension between her and Charlene, and I've never seen a report that Caroline is "protective" of her. She has no reason to favor Jacques and Gabriella over Jazmin and Alexandre -- they're all related to her in the exact same way and to the same degree.
And, she is not a young woman. If something happened to Albert tomorrow, Caroline would be 75 before Jacques turned 18. (And whoever is regent would likely have to stay on the job a few years beyond that while he finishes his education.) We have no reason to think she's not in robust good health, but taking on that role as a senior citizen is not for everyone.
Re: -- A 20-year-old son who could (theoretically) be legitimized and whose recent media appearances suggest a possible interest in a princely role.
The media likes the drama and when is not there, they produce it.
This isn't something the media has ginned up. Alexandre seemed very intelligent and focused in how he answered questions in his Point de Vue interview. He clearly considers his behavior in light of his connection to the reigning prince. (If only all young royal relatives thought that way!)
And, it wasn't the media that put the Monaco flag and crest on his birthday cake. Nor was it the media that had his sister refer to him as "my prince."
Someone is thinking about these things other than the media.
Prince Albert's side affairs are a family issue, like any married man with children outside the marriage. Albert and Charlene's eight-year-old children are a family issue and a government of Monaco issue. They are named since birth as his only two immediate legitimate successors and followed by Caroline's line. And I bet when they are grown both will have great relations with Alexandre and Jazmin whom themselves could potentially have families of their own by the time the twins are 18.
Albert didn't have "side affairs" -- as Alexandre pointed out, his parents had a relationship when neither was married. (Jazmin's story is slightly different, but Albert did not stray outside of his marriage in that affair.)
While the twins are Albert's legitimate heirs right now, that doesn't mean they always will be. When the time comes, whatever and whoever is the expedient choice for the family and their government will take over.
I'd also point out that we don't know that Caroline's children are even in the succession. As someone pointed out last week, Albert apparently commented years ago that her sons did not seek permission to marry.