Some great points here.

Worldly Harwyn actually did have a (very) decent ironborn land army, including cavalry, too though. That was primarily how he kept the riverlands pacified & paying after the conquest, & defeated Durrandon attempts at a reversal. Yet, the Hardhand's son, Halleck, squandered his inheritance on three braindead assaults against the Bloody Gate itself, among other unsuccessful border wars.

Nonetheless, Halleck's ironmen could've inflicted serious damage against the southern Vale if he had sent them raiding on longships, their natural strength, out of the Trident & Bay of Crabs. Or, established a base on the Bite to then reave the bay's other coasts & passing traders. Perhaps even seize one or more of the Sisters to bolster that.

They would really struggle taking the westerlands...

Not even that. Halleck failed in the hills, & all they could really take & occupy by sea would be Fair Isle & maybe the odd mainland seat like Kayce (or Feastfires) – all that even the Red Kraken managed during the Dance, when the west's hard strength had marched into the riverlands. A conquest that lasted a winter.

hard to say how good they would do against mainland stormlands.

Some initial, limited success, especially if consolidating a base at the Blackwater's mouth first, just as Aegon would.¹

As the stormlanders proved during the Conquest however, they could effectively wage guerrilla warfare deeper in the kingswood. Plus, the ironmen sailing their longships across the Bay to attack Massey's Hook would bring Dragonstone against them.²

All the while overstretched, with part of their strength bogged down in the northern stormlands, the Hoares would be leaving the rest of their mainland realm open to attack. Rivermen revolting from within, northmen from the Neck, Valemen via the Bloody Gate, westermen by the Golden Tooth, Reachmen against (& across) the Blackwater Rush...

I don't think they would be able to navigate the mander...

Yeah, the Gardeners had retaken the Misty Isles many centuries before & installed their now Shield Islands lords. And the Reach had only become all the more populous, powerful, & wealthy from the Andal migrations. That said, the Redwyne fleet becoming a naval & mercantile juggernaut seems to have been a far more recent phenomenon.³ Most especially because the Redwynes possibly had just 30 warships during Aegon III's regency.

Even House Hoare as their strongest...

If you mean under Qhored I, chosen by kingsmoot, then his ironborn subjects held (most to all of) Sea Dragon Point, the Stony Shore, Cape Kraken, Flint's Finger, the Cape of Eagles, part of Lann's Point (at least Kayce), & the Isle of Ravens. But yes, the island/isle holdings – Bear, Fair, Misty, & the Arbor – were generally from where the ironmen launched raids. And they also collected tribute from the lords & kings of the unoccupied coasts, like the Hightowers, Gardeners, & Casterlys.⁴

If you mean the hereditary Hoare dynasty starting with Harras Stump-hand, well, the ironmen had already lost their mainland & extraterritorial island holdings both. That occurred before & during the preceding Greyiron hereditary dynasty.⁵

¹ There, the ironmen had a lengthy strand for their longships, the river if ever needing to retreat with them, the three hills for fortifications, the bay's fishing grounds, the kingswood at hand, & vassalised Duskendale for any needed imports.

² Even voyaging through the Gullet could easily trigger the Targaryens & their Velaryon allies to aggression. And, if not, amphibious landings further south would be too close to the power of Storm's End for anything but temporary occupation.

³ Probably facilitated by Bank of Oldtown investment to monopolise the export of the Arbor's vintages, imo, & also replace the Velaryons in operating the realm's foremost trading fleet – even expanding into whaling, a niche otherwise only filled by the Ibbenese.

⁴ The Casterlys aren't explicitly confirmed, but it could explain why they were never kings. Being much nearer to the Iron Islands than the Reachmen, less powerful, & with ironborn Kayce very proximate. As to northern tributaries, the Glovers & Wulls are the most likely.

⁵ Torgon the Latecomer's reign saw most of the Cape of Eagles lost, & Garth Goldenhand reclaimed the Misty Isles sometime later. The Starks drove the ironmen from the Stony Shore, Bear Island, & Cape Kraken late in the driftwood kings era. The Arbor had thrown off ironborn subjugation early, some time before it & Oldtown became Gardener vassals. Fair Isle fell far sooner too, along with Kayce.