I have replaced my axle seal on the passenger side multiple times and it keeps on leaking, i have a new axle in too. I noticed there was some play in the axle too (in the video) and was wondering why or what could be causing it. If you know please let me know, thank you!

 

Did you fully seat the axle inside the tranny until its lock ring clicked in? Sometimes it takes a bit of force to get it to in completely. Maybe your old axle had something like a small scratch on its shaft surface where the seal was riding on?