I am a detective in Florida and have years of street experience as well.
I can only only really speak to florida specifically but it seems you have two situations here:
First you have the violation to contend with, then you have the conduct of the stop issue.
As for the violation, we don't have bus lanes in the Tampa Area so I don't know what to tell you. I wasn't sure if you got a ticket or not.
As for the stop, I can't see why he brought you back to his car. First off, that is not good officer safety. I want to be in the open and able to reach my weapons if I have to. The only time I bring someone in my car is in the back cage. On a traffic stop I only do it if I am arresting them, searching the car when I'm alone, or if it's raining and they need to sign stuff.
I also wouldn't want to be alone in the front seat with a female unless it was being recorded. That is just for my protection in case there is an allegation made.....that's just reality these days unfortunately.
The officer did have the right to move you, when you are stopped for a violation, even a civil traffic infraction, you are technically "arrested". Miranda isn't required for traffic violations because it is civil/regulatory. If it involves finding drugs, stolen property, bodies, etc. then it becomes criminal.
In the state of Florida it is illegal to leave a child unattended in a motor vehicle, and deadly due to the heat. I would at least ask you to bring the child with you because I wouldn't be comfortable leaving the child in the car; what if you didn't put the brake on and the car started rolling while we were in my car?
It is very dangerous to standing on the side of the road during a traffic stop, officers are killed or maimed all the time doing it, and it is not safe to have the suspects there either because we are responsible for you when you are in our custody. The only time I ask someone to get out is for DUI testing (we move to a parking lot for that), to search, or to arrest them.
The safest way is to leave the suspect(s) in the car. It also makes it harder for them to hurt you that way.
My advice to you would be to call and explain, very nicely, to the officer's supervisor what happened. Maybe it's policy for that agency, maybe they leave it up to each officer. I would advise complaining about the procedure and that you feel it's unsafe rather than complaining about the officer....unless he was really rude or improper.
Citizen complaints are taken seriously. Sometimes there are policy's the officers feel are stupid, but sometimes it takes outsiders or the public to get them changed. Follow up the complaint after a few days and ask about the status of the complaint. Remember who you spoke with. If you feel it was blown off, move up the chain of command until someone takes it seriously.
Remember, in every state, you don't have the right to resist, physically or verbally, even if the arrest is unlawful. You have the right to address it later. You can always file a complaint later and/or sue for damages if the arrest was made in bad faith.
Don't let people tell you to argue or interfere, they are setting you up for trouble. In a bad arrest the charge will be dropped, but the resisting/obstruction charge will almost always still stand. Many times the charges are dropped but the court rules the arrest was based on facts and made in good faith.
Remember, constitutional rights only apply in criminal cases in which there is custodial interrogation. You have move where they say, ID yourself, and answer routine non incriminating questions. Miranda can't be invoked on a traffic stop unless it is about something not related to the infraction and when it come to searching, there are times you can refuse and times you can't, either way the court will review the legality of each search.
Good luck...and safer driving!