Healing HP Between Combats—Use a Wand
Buy a wand of cure light wounds, and use it between battles. You can use this right from 1st level, even before you have spellcasting of your own, without any checks, and a party of four can generally pool wealth together to buy one before even hitting 2nd level.
This will literally handle all the HP-healing the party should need. Frankly, there is no better healing in the game besides the heal spell, which you cannot get as a paladin, so if your party needs more healing than that, then they are just out of luck; Pathfinder just doesn’t offer enough tools to help them. In combat, your job is to just focus on killing threats before they can kill your allies.
Healing Status Conditions Between Combats—Mercies or restoration
Later, when you can, prepare lesser restoration or restoration as needed. Having a scroll of these spells may work better; a wand may be overkill/too expensive. Your paladin mercies will cover some of the conditions that these kinds of spells heal, as well, which makes it less critical to prepare these spells regularly.
Actually, this is one of the very, very few cases where a potion can make sense: a potion of lesser restoration can be drank more swiftly than the spell itself can be cast, and it can be used by all members of the party. Potions are overpriced, but if everyone holds on to just one for a rainy day, that could salvage a very dicey situation.
Healing More Serious Status Conditions—Find a Cleric
Keep in good graces with your church, so you can run to a temple and get a cleric to bust out the bigger condition-healing spells than you can currently cast, like break enchantment before you have 4th-level paladin spells. You could conceivably have a staff to cover these problems, but it would be fantastically expensive (which would definitely cut into your ability to deal or take damage).
Healing in Combat—Do Not Except in the Most Extreme Emergencies
Get your enemies dead first. Combat goes too fast, and your healing is too slow, to attempt to actually bring anyone back to combat-ready in the middle of a fight. Only the heal spell can do that. The only time healing should occur during combat is in an absolute emergency, when that healing is the line between life and death. With how little you can heal, that will be very rare.
The vast majority of combats in Pathfinder are decided in the first two or three rounds. They may linger somewhat longer than that, but by then the fight has almost-always been decided. Giving up a third to a half of your combat presence to partially-undo a single attack against an ally is just a waste of time, and that’s what the numbers work out to. This is always a mistake unless it saves someone’s life.
Improving your Healing—Don’t, You Need Those Resources
This is the harsh reality of this system: paladins are among the weakest classes in the game, combat healing is among the weakest potential tactics one can turn to, and the paladin is not in any way well-suited to trying to do it. Focus on doing what the class can actually try to do—get the enemy dead—and you may actually succeed. But it’s going to take everything you can get to make you good enough at that. You have nothing to spare trying—and failing—to get better at healing.
Your out-of-combat healing is good enough. Your in-combat healing can never be good enough. Therefore, you should not invest any scarce resources into healing more than this. That means no feats, no items, no archetypes devoted to healing. They are, all of them, bad, traps you should not take nor should anyone else.
In particular, definitely do not take the hospitaler archetype. It’s a trap; channel energy is weak and it’s even weaker for a hospitaler than it is for a cleric. The aura of healing is absurdly weak for 11th level.
If you are going to sacrifice your damage output for protecting your allies, the sacred shield archetype is vastly superior, and will actually reduce the damage your allies take by a fair margin (it will also reduce the damage you deal by quite a lot, however, since bastion of good replaces smite evil). But realistically, again, the best approach to keeping your party alive, as far as archetypes are concerned, is to kill your enemies as fast as possible. Your archetype should support that. The sacred shield option would be much better for an oradin than a paladin, since an oradin would have quality spellcasting to replace their smite-boosted attacks.
About Tanking—Pathfinder Has No Such Thing
A note on “tanking”—there is almost-zero ability in Pathfinder to do it properly. You can defend yourself, but you cannot easily offer any active defense for allies. The shield other spell is available to you, you could get Combat Reflexes and Improved Trip and a reach weapon if you wanted, but these things are small and all-too-easily ignored. And if you focus too much on your own defenses, enemies can and should just ignore you and go after your allies, who are simultaneously easier to kill and far more dangerous to leave alive. In order to get enemies’ attention on you (and thus away from your allies), you need to be either scary or annoying enough to demand that attention. Again, for a paladin, that mostly means dealing enough damage that you cannot be ignored.
Ironically, one of the most effective ways to deal damage as a paladin is as an archer. This also makes you somewhat less obviously-tough-to-kill, which may actually work in your favor as your enemies think they can deal with the dangerous archer quickly, and then you turn out to be tougher than expected. However, this seems quite likely to not be what you are looking for, and kind of goes beyond the scope of this question, so I will just leave this here. If you are interested, a question asking about paladin archers would be the place to do so.