Can police stop your car in motion if they don’t have probable cause?

To detain you.... an officer has to have reasonable suspicion to talk to you.  To search or arrest you, they have to have probable cause.  So... you actually have a couple of different things going on here.
Your suppression motion should do the following:
1.  Move to suppress the search or detention because the traffic stop of your vehicle was made without reasonable suspicion or probable cause.  You did not commit a traffic offense.  They did not have a warrant.  So, they did not have a basis for a detention.  Detentions have a lower burden than searches or arrests.  I would suggest arguing that they actually arrested you when they drew their guns and told you to stop.  At that moment, you had a complete loss of liberty more consistent with an arrest... which is a higher burden.  Make the state meet the higher burden. (not the lower detention burden)
2.  Also include in your motion that the police officially arrested you by placing cuffs on you, again, without probable cause.  They don't get to do it backwards.  Your suppression motion should complain of the cuffs as an arrest and thereby force the state to defend the higher burden of probable cause.  They cannot claim they were arresting you for possession of a controlled substance because they did not find substances until after the cuffs were placed on you.
3.  Finally, your motion should include a paragraph or two complaining about the search of your pockets.  Texas courts of appeals have generally permitted officers to conduct "pat downs" of individuals suspected of criminal activity or for officer saftey.  However, a general pat down does not authorize them to reach and scoop out the contents of your pocket.  That is a search, even under Texas' version of search and seizure law.
The case is beatable just depending on what other facts they had.  If they had probable cause to believe that you were aiding and abetting a fugitive, then they could also charge you with hindering apprehension of your cousin.  However, they didn't do that.  They probably didn't do that because you didn't have knowledge of your cousin's warrant (and/or they don't have proof that you had knowledge.)  Considering they did not charge you with this offense actually helps improve the chances of your supression motion being successful.  However, without reading the actual offense reports, I cannot give you more precise prediction about the success of the motion.