You're not going to get the axles seated by pressing on them from the suspension side. You actually need to try and force the inner axle joint into the differential. It's kinda hard to do, because if you hit it with a hammer you risk tearing the axle boot. Take a look at the axle dust caps, see if they are flush with the differential.
If you don't know what the dust caps are, they are the (usually) brass colored round discs that are at the end of the inner joints on the axles. They should look flush or at least very close to flush with the differential. DO NOT HIT THE DUST CAPS, they will slide on the axle and do you nothing but headache, if you do that then you'll have to remove the axles to reseat the caps again.
Just try to force the axles in to the differential, worst case scenario you can't do it the way I've described, and you'll have to remove the axle and slam it in again.