There is a very simple rule in this type of situation, nuts are replaceable, but if you damage or break off that particular bolt (or the other three like it) you are in serious trouble. There is no point in trying to get cute or just hope the nut will eventually loosen somehow maybe with enough penetrating oil and a little more force. Sacrifice the nut. In the climate and conditions where I live, namely Nova Scotia, seized nuts and bolts even on cars not that old are a fact of life. The location of the seized nut (as I can see in the photo) gives you several options to cut the nut to remove it. One possibility is to cut off one or two sides of the nut, being very careful not to get down to the bolt threads. You could use a small angle grinder with a thin cutoff wheel and carefully slice off at least one side of the nut, and of course not too close to the bolt. In most cases just removing material from the nut will weaken it and it may come off with a regular socket, or even better, one of the special sockets designed for use on damaged nuts (or bolts). Rather than an angle grinder I would use my electric cut-off grinder (smaller than an angle grinder and that takes fairly thin small diameter disks). However in your case my preference would be using one of my air-powered die grinders, and I have a good collection of carbide cutters for them. With a die grinder and a small cutter you can make a groove in two flats of the nuts (not down to the threads of course) and then you may find the nut has weakened and can be removed with large pliers, etc. If it doesn't you can take a small cold chisel and position the chisel at an angle in one of the groves of the nut, in the direction the nut would unscrew, (so not pointing directly at the bolt) and give it a hit. In that situation I use an air chisel, positioned similarly to the cold chisel, and usually one brief snap of the air chisel will split the nut and it will probably fall off.
Of course even with all 4 nuts removed there is a good chance that the bolt is seized on the inner sleeve of the bushing that really holds the frame on. However, you will be replacing the old piece with a new one so you don't care how much you butcher the one on the vehicle to get it off. You may have to slice each of the 4 housings around the support bushings to get the old frame off, then chew off the rubber bushings to get down to any of the seized inner sleeves. At that point you will spray whatever anti-seize liquid you've got, at the top of the sleeve, let it work then try pliers or something similar to try to twist the sleeve around the bolt to free it. Once you can do that the sleeve can be removed. In the worst case you will have to carefully grind away a small region one side of the seized sleeve, also being careful not to damage the bolt. The last thing you really should do before installing the replacement frame is to use the proper die to clean up the threads on the 4 bolts.
I know some oxyacetylene enthusiasts will recommend cutting the nut off that way but I don't have that set up, don't want it. Using acetylene is tricky in order to avoid damaging components around the target, especially in your situation, and also setting stuff on fire. As well, you'd better be sure you have a fire extinguisher handy and live near a fire station if you choose that method.
