Alright, so I feel a bit of backstory is in order, but I'll try my best to tldr at the end. Tons of spoilers head if you have not played.

I've been DMing pathfinder for about 6 months now. I understand the mechanical rules rather well, but I've recently felt like there's a bit of an issue while running RotRL. I've been running it very close to as written, changing only a few things to make it easier on the party. The party consists of a Bloodrager (building into Dragon Disciple), a Kensai Bladebound Magus, an Arcanist, and a Rogue. I know it's not exactly the ideal party set up, without a divine caster they are really feeling each hit.

That said when we first began the campaign I did a survey with them to get a feel for what they wanted. All of them said combat wise they want it to be fair, don't run it easy but also don't go crazy and make the monsters as hard as they possibly can be. The party first got stuck in the catacombs of wrath, taking 4 days, and 4 separate sessions to get though it. First time they went right to the boss, used most of the spells on her then switched to the adds, she healed up while they were dealing with that and by the end they could only deal 8dmg max with roughly 25% hit chance, which she healed 2 a turn. They left as they were simply taking 1-2 damage a turn and not doing any. The next time after figuring out what she is they entered into her lair again and due to an unfortunate crit they lost a party member and were in the end forced to retreat. The final time they were doing alright but I allowed a bleed from a crit to stay on even though the fast healing should have stopped it. They brought her low, but she ran away and passed out. Things continue from normal there except the town seals the tunnel.

Last session I had them level up to 3 and they finally made their way to thistletop, where a party member proceeded directly from c27 (hole in to the water below) to c4(10 golbin fight) before I could even describe the scenery. So the fight started and I had several goblins rush them while the others in the back too out bows. I'll admit I could have played the goblins a lot stupider, but they their plan was to lure them out of the area, however they made almost no verbal attempt to do so, just kept moving backwards. All the arrows were fired at the heaviest armored character, and I had the goblins attack whatever last hit them, or whatever was in range. At the end of the fight they were down to half health on one character, and 1 HP on the bloodrager. They used their few healing items, but after that they proceeded towards the dog kennels (c5). I actually chained 4 dogs there rather than let them run free, I knew they would die if I did not. They proceeded to rile the dogs, and shot one several times, which I had Gogmurt get alerted. I had him cast entangle turn 2 in order to give the party a chance to get to him, and from there he basically just used melee attacks or his wand of produce flames. The fight continues, he ends up ducking into the bush, heals, then summons an eagle and attacks them once more. They get him low, but do not kill him, so as per the book I have him run away to the bridge as he has a clear exit. They did not pursue, and are now at very low health pools, with almost no spells, so they decided to head back to sandpoint to get healed and spend the rest of the day there.

Now, this is where I have my problem, I'd imagine realistically there would be something that would happen when the PCs show up, let a villain alert the others, than leave for the rest of the day. Currently I fear that if I play the encounter as written it may result in a tpk, let alone make it any more difficult. They haven't been complaining, and I've recently asked how everyone is liking things and they said it was good, but I can feel a bit of morale loss and clearly see they are struggling. They've said they want more gold, but other than the loot off Elyrium I have given them all of the loot, and even allowed them to earn an extra 200 or so. I want this to be fun for them, but I also want them to become better players. We didn't enjoy it when another friend DM'd and had the fights basically be a complete joke. I've been slowly nerfing things, less hp, not using feats, but it seems if it's too easy they don't even remember or care about what they've done (Goblin in the wrath cave had TWF removed, they barely remember the fight).

I suppose my question is, should I be nerfing things or just run it as written? If I should, what do you recommend doing not to make combat trivial but still challenging? I want to try to keep immersion best I can, as I know that can be important for my players.

tl;dr : Party says they want a fair game, struggling on a lot of content even with nerfs, no complaints about it but fairly obvious morale decline, how should I make it more enjoyable?

Edit: Thanks for all the suggestions everyone, I think I know exactly how I can handle it where I tackle all the issues we have at the same time.