There are very few hotels with kitchenettes. Most people don't cook (and don't want to cook) on vacation. Most hotels also don't cater to the low-income, and folks who cook on travel tend to be low-income. There's business rentals that offer this, but they're often not bookable for short-terms (usually 2+ weeks minimum).
Most hotels can accommodate 5+ people in a room, if you call them. Though no rooms (except suites) will have more than 2 beds, hotels will provide cots. In general, though, rooms aren't expected to host any more than that, and if you have more people than that, the expectation is that you'd book more than one room. Plenty of hotels have adjoining rooms for this purpose.
Again, though, hotels aren't really targeting low-income folks. Airbnbs can be cheaper in this regard, but most rentals on Airbnb charge by the person, so in some cases can be as expensive or more expensive than getting 2 rooms.
In either case, I think the issue is your needs are uncommon for vacation travel.