I have two deep cycle batteries in my Airstream, in the panel there is a fused bus bar (that appears to be faulty) so the solar panels only charge the one battery. Can I just run a heavy gauge wire between the two positive and two negative terminals? Or do I have to put a fuse across them? ... if so do I fuse the positive or fuse the negative? What's the worst that can happen if I don’t fuse them?
Remember that in a DC power system like you have, fuses prevent electrical fires by protecting WIRES, not the devices connected by the wires. This is not to say that blowing a fuse never prevents damage to an attached device, but that the "correct" way to think about circuit protection is to examine the circuit topology and identify faults which could result in a "wire" being subjected to current (and hence temperature) sufficient to start a fire, either in the insulation or in a device connected to the wire in question. This includes all fault modes identifiable. In particular, this includes at least damage to insulation from abrasion, thermal stress, water absorption, and chemicals (oil, gasoline, solvents), also parts and tools being dropped into a panel or battery box.
One other case to consider is that a fuse performing its act of protection can lead directly to a fault as well. If you have never seen one of the big T-series 400amp fuses go bang! you have likely saved pair of underwear. Fuses blow by melting metal, producing liquid metal which can be ejected to land on some other connections causing another fuse to blow. This is why fuse enclosures are worth paying to get quality products.
The worst case scenario is one of the cells is shorted and before it explodes/catches fire itself it also shorts the other cell.
The fuses are there for a reason (and there is a reason the fuse went open).
Sure, you "can" bypass the fuse with heavy gauge wire, but you will take the risk.
It is very common to have two or more lead-acid batteries in parallel, with no fuses between the batteries - but you MUST have a fuse close to the batteries, between them and other wiring in the boat/vehicle. For marine use, ABYC says the fuse must be within 7 inches of the battery.
I have had a couple of cases where one cell in one of the paralleled batteries shorted - there was no fire,explosion or other excitement - I just couldn't charge the battery bank to its proper voltage.