Trying to trouble shoot a problem please help.

So for about a month now I have been having intermittent "rubber-banding" while playing FFXIV. The Issue only seems to be on FFXIV. The game seems to freeze for a few seconds with a maximum of about 20 seconds. During that time my character can move around but is unable to interact or do anything. Any cool downs I pop are lost and I don't get the buff when the "rubber-banding" catches up and all the animations go off at once. Now when I say "rubber-banding" when it catches up my character does not rubber band back to the spot were it started because one time I lagged at the end of that see of clouds dungeon were you can fall off the edge and normally die but I did not die and was running around alive on the bottom of the pit when the it caught up again had to use the return spell to get out. My room mate and I play on Bryhildr sever ps4. While this can happen at anytime its most noticeable in a party rather then slow play since you see the other players and npcs freeze. So here is what I know about the problem.

ISP is time Warner cable. They have a monopoly were I'm at so switching service is no option.
The problem is on the ps4 and it is effecting me and my room mate when we play on either of our ps4s.
It's not the modem we have replaced it with a different type and still have the problem.
Its not the router because when we bypass the router and go directly to the modem its still happening.
Its not our cable line because we have had time Warner techs out here 3 times trying to fix it and have replaced everything.
Heres what I don't understand. My roommate and I can take our ps4s over to my mothers apartment (she also has Time Warner ISP but pays for a slower speed then us) and play on her internet in the same apartment complex without ANY issues.

Anyone have any idea what could be causing this or how to fix it? Thanks in advance.

Update: Timer Warner sent a tech and maintenance worker to try to diagnose the problem as well. No new answers even with the new Time Warner rental modem. The maintenance worker says its not the "Tap" and the tech could not find anything in the apartment wrong. At least now a tech was able to see the problem when I tried to play the game this time but that doesn't help. Am I going to be forced to literally move to anther apartment if I want to play this game at home?