You were cross axled. The way 4x4 works in a part time 4x4 like a Daihatsu is this. When you engage 4x4 the transfur box puts 50% of the drive to each axle. The diffs then supply this to each wheel. As with a 2 wheel drive if one wheel on an axle losses grip and spines all the drive goes that way. With a 4x4 one wheel on each axle has to lose grip for this to be a problem. Cross axeling is the most common cause of this.
The locking hubs are on the front wheels to alow the front diff, half shafts and prop to be totaly disconected when not in use. If the front wheel in the air was spinning, these were working.
I'm not aware that there is a limited slip diff to fit the Daihatsu 4x4's. Though there may well be an aftermarket option out there. It is posible to get locking diffs fitted, but they are very hard to come by I'm lead to belive.
If you are only going to fid yourself in this position occasionally, then driving style may be all you need to adjust. You can offten get out of a cross axle by jabbing the break peddel with you left foot while giving her about half revs with the right. This is like a really bad manual traction control. By applying break to the spinning wheels, some drive is forced to the non spinning ones. The ones with grip. The problem is they are being breaked to, so you need to keep the reves up to prevent stalling.
Also rocking the car can free you. Alow the car to roll back from the cross axle drive into it again. As soon as the wheels lose traction, dip the clutch. Alow it to roll back again. Keep repeating this, giving it more rev each time until you find the right speed so enertia takes you over the obstcal. Be ware not to give it too much umpf when the tyes are loosing traction, or to alow the roll back to happen with you still powering forward. The sudden grip in the wronge direction this cuses can be quite damaging to the drive train.

Any veiws expresed in this thread by me are purely from my own experience, and (sometimes) falible memory. Hope my comments help, but please don't take them as gospel.