Hi, Kevin! Sorry nobody jumped into this question, your photos and questions did post...I'll answer personally.
The inner seal is a light tap/fit with a suitable driver. Often, you can find a large socket that will work here. The seal must be driven squarely into the bore. There should be some resistance, not a lot though or the seal will distort. If the seal has a coated jacket, you do not need to add sealant at the outer edge of the jacket. If there is no coating, put a film of Permatex 3D or Super Flex on the outer jacket face before driving the seal into position. Look in the bore, you should see where the original seal jacket aligned. You'll drive the new seal into that position in the bore.
The outer flange seal has the raised portion of the seal facing outward. The flat surface faces inward. In your two detailed photos, the first photo (on the left) is how the flange seal should appear when installed. The thin lip of the seal is a dust barrier, and the heavier lip is the actual oil seal.
In the case of the inner and outer seal, make note of the heavier oil seal lips. The flare of the seal's lip faces inward in each case. This is to retain oil. Imagine placing the seal in "backwards". The oil would easily press past the seal lip. With the seal lips facing inward, they contain the oil.
An example: On engine seals, where there is pressure in the crankcase, the lip also faces inward. The pressure within the crankcase makes the seal lip press against the shaft. Envision placing the seal in backward at the timing cover or crankshaft rear main seal. The lip would open or spread from internal crankcase pressure, and oil would pour from the seal.
So, again, make sure the flared seal lips face inward on both axle seals. Try to position the inner seal close to where it rode on the axle shaft originally. If there is a noticeable seal groove on the axle shaft, you may be able to adjust the seal's position slightly to run on a fresh section of the axle shaft's polished surface.
Make certain that you pack the axle shaft bearings properly! If you note the design, the bearing is outboard (outward) of the inner axle shaft seal and inboard (inside) the outer flange seal. In this space, there is no axle shaft lubricant reaching the bearing. (The inner seal prevents this from occurring.) The lifespan of the axle shaft bearing(s) depend upon proper grease packing of each axle shaft bearing. There is no provision for lubricating these axle shaft bearings other than removing the axle shaft. IF lubed properly, the bearing and grease will go a long while between services. If you need tips on bearing packing, please ask...
I'll watch for your reply and questions, Kevin. We'll make sure you get a prompt response! Thanks for participating at the forums, we look forward to your topics and posts.