Would Historia Reiss become as big as Rod Reiss if she had turned into a titan? The humans become Titans through the use of an injected medicine, and the Titan form they take is due to the type of medicine injected. Therefore, it can be deduced Bertolt Hoover got an injection that gave him the gigantic form.
Case evidence is Rod Reiss, who became a Titan that is even bigger than Bertolt after he licked the spilled injection that he was trying to give to Historia.

Source
If so, does that mean Historia Reiss would have become a titan of the same size (or maybe even bigger since she would have been injected with the whole serum unlike Rod Reiss that only licked a bit) as her father?
That would kill Eren and Rod seeing as everyone died when Ross transformed except the ones protected by the hardening ability and Kenny who managed to get out but died short after from injuries as seen in the recent episode.
She wouldn't even be able to eat Eren that way and take his titan shifting power and the coordinate since he would be vaporized by all the heat and burried under the wreckage. So she would stay as a mindless titan.
I don't think Rod would want to die by it too so either he didn't knew it would be that big since the other times the ceremony happened the titan was smaller, or she simply wouldn't become that big (for some unexplainable reason or something that I'm not aware of).
In the same topic, from the manga spoilers that I have seen:

 If the mindless titans are in fact Marleyans traitors injected with the titan serum, shouldn't there exist some (during all these years) that would also become extremely bigger than the usual ones and become a threat to the walls?

My best guess is that this was missed out by the story writters, or that it would be explained in the future, or because the plot demanded it, or rule of cool. But I could be wrong.
This source, this one and this Reddit page might be important to the question.
The serum, which Rod Reiss wanted to inject Historia with, is definitely a powerful one. Seems like it contained powers like burning things around you (on your command) and turning yourself into a giant Titan form. 


  Does that mean Historia Reiss would have become a titan of the same
  size (or maybe even bigger since she would have been injected with the
  whole serum unlike Rod Reiss that only licked a bit) as her father?


I don't think so. The Rod Reiss titan was abnormal. He wasn't even able to walk properly and was dragging himself on the ground. Rod Reiss licked only a little bit of the serum. If he had injected the whole serum, he would be just like a normal (dumb) but a powerful Titan. We have seen from the beginning that the correct way to turn someone into a Titan is to inject them with the whole serum (Eren's case, Rod Reiss family's case). Rod Reiss also wanted to inject the serum to Historia, but Historia wasted the serum so Rod Reiss had no option but to lick it from the ground. 

So if the serum was properly inject to Historia, she wouldn't have become such a huge abnormal Titan. She would've been a normal, a powerful Titan and would've chosen to eat Eren (he was the easy target)

The reddit link you provided also agrees that


  Wrongful injection of titan fluid is my theory. He licked it, didn't inject it with a needle.


Let's also take the proof from the anime. When Levi confronted Kenny on the verge of death and asked why he hasn't injected himself with the serum considering the burns and the blood loss, Kenny replies


  Yeah, I wonder. If I don't inject it right, I might end up like he did (Rod Reiss), all messed up...




So to summarize all of this, Historia might have had the giant Titan form but not as abnormal as Rod Reiss, she would be a controlled Titan. She would've definitely eaten Eren and taken his powers!