So a few comments and potential suggestions to ponder.
First, I advise against adding class levels to monsters as a means of beefing them up or making them special. It is a tempting prospect, but is counterintuitive to the process for a few reasons. It over complicates monsters with a bunch of fiddly bits and passive bonuses that make then more difficult to run and most of these are frankly things that players will never notice due to them being under the hood. Additionally, player classes are designed intentionally to be class cannons in nature (even the tanks), meaning they dish out damage, bit cannot take it near as well. This is the exact opposite of what you want when designing a monster, particularly a "boss" as they are designed to take hits and deal damage in a way that hopefully won't tpk the players.
You are better off adding more health, or defensive abilities to make a monster stronger than the standard succubus. Alternatively, add the ability for her to cast warlock spells and give her a few of the invocations that make sense if you want. It still gives the warlock vibe and gives her the concept of having a bit more magic utility compared to the standard succubus. However, ALL of these needs to be balanced according to the charts listed in the DMG. Figure out how powerfull you want her to be first, then alter the stats to get her there.
Second, to answer your question, there is nothing that states directly according to the charm ability that she cannot use it on a target through her familiar if she can see them. However in the familiar ability itself, it does only allow you to cast spells, not other abilities. Charm is not a spell. If you wish to add a custom invocation for her, that is an option (though again I'd advise you to just do the above instead of class levels).
...that said, while RAW kind of allows it and the charm doesn't require a succubus to be seen to charm someone, RAI is arguably different. In literally every source of fantasy setting and folklore/legends involving succubi, they use their bodies to seduce those attracted to them (usually men, but not always). While sometimes this occurs in dreams (the main reason they don't require the succubi mechanically to be seen), even in those cases they appear *in* the dreams of the person being seduced. The original concept of succubi in folklore comes from two sources, explaining sleep paralysis and women seducing men to gain something from them. D&D from a mechanical sense has decided to make night hags fulfill this former role, while the succubus fulfills the second. There is a reason both monsters have the ethereal ability and are similar, but each have a specialized ability to fulfill this role.
In essence, this means that the succubus monster as written uses their body to seduce someone, implying that they are seen by the person being seduced. This would make them seducing someone through a familiar...strange. The entire essence of this monster is to appear before a person and seduce them visually. It is the core concept for it, and to do it indirectly is to arguably make it no longer a succubus, but a random fiend who charms others. To say nothing of the idea of the players being on the receiving end of an ability that would be most frustrating. The ethereal ability is already a potent tool for her to hit and run. She can appear before the fighter (or any player alone), seduce them, and shift back away to escape with very little chance of being stopped short of powerful magic.
Third, and a minor gripe, a devil/demon themselves becoming an actual warlock, a person who has sworn a pact with a greater power, is a bit weird. They are the sort to *give* Faustian bargains, not make them. There are a number of ways you could perhaps explain it admittedly though (perhaps she's sworn to a more powerful succubus / devil? Hopefully you've put thought into this).
Hope it helps.
