I see that you want to stay a pure paladin, but I’m afraid I simply cannot recommend that. Feel free to ignore this answer if you really must, but a healer/tank paladin really wants to multiclass oracle. Pure paladin is just not very good at this. But paladin is a very good start to doing this.
Specifically, paladin is great for tanking thanks to divine grace. That is a fantastic ability. But paladin doesn’t have much more to offer for tanking or healing once you have that (if we’re being honest, it doesn’t offer much of anything once you have that—paladin is not a very good class).
But a paladin foundation can make for an extremely tough oracle. You have a bit more HP, and you have heavy armor proficiency, on top of divine grace adding your Charisma to every saving throw. Oracle then allows you to have strong spellcasting, also using your Charisma, and the mysteries can even find more uses for Charisma, such as the several mysteries that replace your Dexterity to AC with Charisma to AC (this is still limited by your armor, so if you go this way you may still want to use light armor even though paladin allows you to use heavy armor).
This so-called “oradin” is still a paladin. You would still need to adhere to the Code of Conduct, and also being an oracle would not change that. Even having only two levels of paladin, which is what I recommend, does not change that. What these things would change is that instead of martial prowess and damage-dealing, you would have much-superior spells—which is good, since it allows for better healing, better protection, and better support. In short, multiclassing oracle is how you make a more support-oriented paladin. The paladin features you miss out on are mostly best used for damage-dealing.
On which note, let me caution you against taking the title “healer” too literally. The cure wounds spell line is very, very inefficient. You may be called upon to cast those spells in emergencies, but the way things work out in Pathfinder, you are always better off protecting your allies from future harm (by buffing them, debuffing enemies, or applying some effect that separates one from the other) than trying to heal.
Instead, I recommend that you use a wand of cure light wounds (which you can use without a check since cure light wounds is on both the oracle and paladin spell lists) to keep everyone fit and ready in between combats, and only cast cure wounds spells in emergencies (probably just cure light wounds to get someone back into positive HP). Even with the life mystery available to potentially improve them, they just aren’t good spells.
The one exception here is the heal spell. That spell is incredible, and you should learn it ASAP. Once you know it, you will be able to heal huge chunks of HP at a time, while simultaneously removing a lot of negative conditions.
On that subject, spells that cure long-lasting adverse conditions, such as restoration, may be worth learning. They’re more expensive in wand form, and if they come up often enough, being able to heal them is very much worthwhile. In fact, it’s the most important kind of healing in the game.
But most of your spells should be about supporting, protecting, and enabling your party members.
To this end, I much prefer the sacred shield paladin archetype to the more apparently-appropriate hospitaler. The bastion of good ability is far more appropriate and useful to you than smite evil would be. The holy shield feature is also pretty solid, but I would recommend going for oracle before then.
For the oracle, the base version of the class is just fine for you; the warsighted oracle archetype is kind of interesting, and might recapture some of the martial ability lost when leaving the paladin class, but personally I would suggest that revelations are better than combat feats. Oddly enough, the black blood oracle archetype is also worth considering: the dark resilience revelation offers you greater protection against effects which could take you (the party’s healer) out of the running (leaving no one to heal you). It has some potentially-awkward fluff implications, but the black blood could also explain why you are taking a somewhat unusual approach to paladining than others might.
For mysteries and revelations,
The battle mystery has obvious appropriateness, and the battlecry revelation certainly does help out your allies. Battlefield clarity and war sight both help you stay up and available to support your allies, which can be important. And combat healer can actually kinda-sorta make cure wounds spells worthwhile, though it is so sharply limited in how much you can use it that I’m not sure I can actually recommend it.
Life is perhaps even more obvious. Unfortunately, since healing is inefficient, the life mystery is kind of meh, though it gets enough to be worth considering. Combat healer returns as an option, though again not as good an option as you might hope. Channel is likewise not all that great at healing, though it’s not awful. Enhanced cures could be amazing (if it’s allowed to apply to cure spells cast from a wand) or worthless (if not); ask your GM. Life link is OK but not amazing. Safe curing should be unnecessary. Spirit boost is meh until you get the heal spell, at which point is becomes quite good; I’d probably wait until I got that.
Nature has one of the Charisma-to-AC revelations, nature’s whispers, and it also has transcendental bond, which is great for organizing your party and even allows some otherwise-touch-range healing or buffing from a distance. Bonded mount also allows you to replicate some of your lost paladin class features, which is nice.
Time has the speed or slow time revelation, which is amazing for you since haste is not otherwise on the oracle spell list. That alone is a strong reason to consider this mystery. Temporal celerity can help you to get your buffs on allies at the start of combat, which is excellent, and rewind time can keep you going when you might otherwise be taken out of a fight. Time sight is also extremely useful to your party.
Personally, my recommendation is the time mystery. It hits a ton of high points for you.
Finally, if you are not playing in Golarion, you might consider the Divine Fighting Technique feat: the style associated with Desna in Golarion could be very nice for you, letting you use Charisma for attack and damage as well as AC and saving throws. Desna is a CG goddess, which is why this doesn’t work in Golarion, but if you aren’t there, maybe it could be associated with an LG deity.