The only way to influence Trump's policy at this time is to be on his side. This may sound weird and very counter to prevailing thought but this may be the only way. Trump already knows he can't win the other side so he will continue to appease his base which will be more detrimental to all of us.
It depends on what you mean by "his side". If you mean the Republican party (which is not really "on his side"), then you're right, they are in the best position to fight him. And they will do so if they hear a groundswell from their constituents that "this is not us". I am cautiously optimistic that this may happen. The condemnation of a number of senators, and probably more importantly, a bunch of Christian organizations, is a good sign.