Every time I try to adopt a pet, it makes a error in the social worker and him/her resets (I have the errortrap). I can not get the pet to come to my house, although I choose the name and the notification appears that he is coming and everything. The error with social worker always comes some time after the notification saying that the pet is going to my house.

Hi there. The pet adoption social worker getting "lost" with the pet along the way is a known glitch with the game that has been there since just about forever. The best solution is to never use that scenario. This is one of those things with the game that was a good idea, but it often just doesn't work right. You can choose from the same pets by using the MasterController interaction instead, and the pet will materialize on your sim's home lot without the social worker firing.
NRaas > MC > (Sim) > Basic > Adopt Pet
(game must not be paused when running this command)

It's the same with adopting a child, the equivalent MC command works much better than the often broken social worker by phone one.

Not really related to the errors you are getting, but many of your NRaas mods are outdated and I would suggest replacing them with current versions.
GoHere
MasterController (2 versions behind)
MasterController Cheats (same)
Overwatch (3 versions behind)
Register (huge update, fixed some major bugs)
StoryProgression
StoryProgression Population
StoryProgression Relationship (this one is up to date, but is newer than the previous two; the mismatch can cause problems)
Traveler (huge update, fixed some major bugs)

Also, please stop uploading your ErrorTrap log. We got it several time already.

It's a shame that we have to use mods to simulate some of the game's very simple features. I will update all my mods to see if it solves the problem. I'm sorry for the uploads, I forgot how the system really works. In the file it is not possible to see if it has some mod causing some conflict? The "why" has the social worker been restarted? I looked but did not come to any conclusions.

This happens to players with no mods in play at all just the same, it's not a conflict issue. If anything, GoHere should make it less likely. What the script log tells us is that the adoption social worker is unable to route through the world as she must from her assigned spawning point in order to get to your sim's home. This is where the scenario is failing, I've added the bolding for emphasis.

System.NullReferenceException: A null value was found where an object instance was required.
#0: 0x00010 callvirt in Sims3.Gameplay.Objects.Vehicles.Sims3.Gameplay.Objects.Vehicles.CarNpcManager:DriveFromPointToMatrix (Sims3.Gameplay.Objects.Vehicles.Car,Sims3.SimIFace.Vector3,Sims3.SimIFace.Matrix44) (4222DB70 [52223260] [vt:41C9A494] [vt:41C9A4A4] )
#1: 0x0005a call in Sims3.Gameplay.Objects.Vehicles.Sims3.Gameplay.Objects.Vehicles.CarNpcManager:DriveFromPointToMatrixWithinTime

It doesn't always fail for all players. But you are playing in Starlight Shores, a world that is known to have mild world lot routing issues already and I take it that both adoption scenarios must be more prone to failure there or at least on certain parts of the map. I've had this one fail in Riverview as well though, and stopped trying it. Actually I was able to pinpoint where the pet adoption social worker was failing that time, coincidentally he happened to be spawning with my sim's dog not far from their house so I could watch it happen, and after around 12 reloads and re-tries (I was being stubborn myself) I was able to wrestle the dog away from him before he disappeared permanently. I'm not going through that again, but for whatever reason it became a challenge that night -- and it took ALL night.

Years ago, Twallan investigated these errors (before Pets even came out so he would have been working with the regular adoptions first) and determined that providing the MasterController ways of getting through them are much less stressful than trying to sort out every possible world lot flaw that could ever trigger them. Updating your mods is not likely going to help here, that was for other reasons and so we can provide better support should other issues arise.

The adoption social worker scenarios are cute when they do work correctly, but very brief. The Service Sim does not stay on the lot for very long, and a real time minute or two later you end up with the same child or pet that you can get the MC way without all the fuss.

I understand, Thanks for explaing to me, I have no idea of all of this. EA should care more about that kind of stuff. I am glad that Nrass exist for helping us a lot with the game mechanics.