How do you remove self-tapping screws from RV frame?

You will need a carbide drill bit to drill thru hardened screws. Low cost masonry drills are carbide tipped if you can find one small enough. Any machine shop supply house will have carbide in the size you need if you can't find a suitable masonry drill. For a novice, I recommend the spade type drill as they will not break easily. Run carbide drills at a high RPM.

suggestion

I've used an air hammer on them with just the right-size flat point. I good air hammer will flat-strip the threads right out. Then, I drilled and tapped to the next size up.

Depending on how thick the metal is that the screws are broken off in..if the metal is .125 or less, I would take a decent punch and pound them through.

Are these the fine thread guys with a drill point? It was all I could do to remove four that were holding a battery rack together. If you have a travel trailer frame, steel around 1/8" thick, you might get them out with a penetrant soaking, and I like to beat on the ends. Seems to jar the threads loose. I have not tried this, but for those that still have heads, I wonder about an electric screw impact driver, like you'd use for wooden deck boards.

The things are hard hard hard and meant to be driven with a power tool at about a million RPM. We have some through our Ford E450 chassis that's 5/16" thick. I have NO expectation of doing anything with them but leave alone or break off.

Based on recent experience with HF "nitride" drill bits, the screws are tougher than any HF bit or extractor.

Those self-tapping screws are really hard, and it may be much easier to drill new holes than try to remove broken screws. An easy out isn't such a good idea since if you break one of those you will not be getting it out without a ton of work.

I think the vice grips on the back side is probably the best idea.

We are discussing self-tapping screws aren't we?

If you thought drilling the frame was difficult, drilling into a fastener will be another level harder. If it was me, I'd grind the screws off with a 4" grinder and drill in new locations for screws.

If you are having difficulty with bits, slow your speed down and put less torque on the bit. DEpending on what size hole you need, drilling a pilot hole can sometimes be a labor saver.

Depending how thick the screws are, you can use a Screw Extractor
They're available at many places, Harbor Freight, Big Box Stores, Hardware stores.

An EZ-out sort of screw extractor may work if you can't get at the back of the screw.

Can you get to the back side of the screws? If so, soak for a couple of days with a good penetrating oil and then use vice grips to remove.