I think you need to tread carefully.
It seems that trying to create such a combination would have the potential to become incredibly overpowered/unbalanced very easily.
You want it to be a half caster + Warlock abilities, which I presume includes invocations. So 'at will magical powers' on top of a full half-caster suit of spells + sub-class [patron & pact] features. That is, already and in itself, more powerful than a warlock.
If you want paladin mixed in there as well, are you increasing the armor and weapon options? On top of half-caster spell slots/known/progression and warlock invocations and at will abilities? Are this arcane-half-caster's spells going to be Prepared like arcane casters (in which case they can accumulate any/every spell you want) or limited selection of known spells to use with your slots like a ranger/sorcerer or "everything known/prepare what you want" like a paladin? Or the warlock table, more spells known than a paladin or ranger but with significantly limited slots to use each short rest?
It sounds like a very easy way to overpower pretty much all of its proposed parts.
I think the idea of a true half-[arcane]caster is great and the game can certainly use one. IMHO, for 5e, the Bard could/should have been that, quite handily. But the developers didn't go that way.
To do what you propose, look at the half-casters we already have. A paladin gets its half-caster slots and progression, +full armor & weapons, + martial stuff (access to a selection of thematic Fighting Styles & Extra Attack) , +Channeling, + extra oath/domain spells, + roughly 6 additional (beyond spells and channeling: Auras/Divine Sense/etc...) misc. magic abilities.
This is the "half-caster" with the magic dial turned way up. The martial dial is also turned all of way up.
The Ranger, as has been complained about from its release, by the book is relatively underpowered as compared to their spiritual half-caster brother-class, the Paladin. Discounting the absolute mess of the Beastmaster for the moment and just using the Hunter...
They too receive half-caster slots/progression, + all weapons, only 2/3rds armor though, + wilderness/exploration traits, + martial stuff (thematic selection of Fighting Styles & Extra Attack), + more martial stuff (their Favored Enemies stuff, special attack & defense moves, Foe Slayer capstone), + roughly 6 misc. magic abilities.
The rangers strike me as the class they did with the martial dial turned mostly up. Similarly, the half-caster nature and progression of the ranger gives them a heavy magic feel/flavor. But both the martial and magic dials are definitely turned down as compared to the paladin.
If you want to wrap in Warlock abilities, the pool includes: cutting armor to 1/3rd (light only), weapons to Simple only, limited slots per rest (vs. half-caster progression), + pact feature, + extra patron-dependent spells known, + invocations, + roughly 6 misc. [4 of which are patron thematic] magical abilities.
This is the class that has the martial dial turned almost to "0" (light armor only, simple weapons) and the magic dial turned way up. Comparable to a Paladin as far as magical abilities, in most respects, as is, but significantly limited in their potential slots. The at-will invocations more than make up for the slack of slots.
I think, if you want an arcane half-caster, then do that. Take a ranger or paladin and make them arcane-based. Swap out [or create new] features for the base and sub-classes, one-for-one to reflavor things to arcane/wizardly magic, as you wish, leave in the martial/combat stuff, and have a legit "half-caster/half-warrior" arcane class.
Kind of, like, an Eldritch Knight or Paladin level of martial, but with the spell-use turned up [to half-caster]. That makes a comparable class. The invocations and other warlock shtick puts it over the "balanced" top unless you are going to severely restrict the martial side of things...in which case then you don't really get that paladin/ranger/"half-caster" vibe.
Look forward to seeing what you come up with. Good luck.