Find gaussian in data
Still not making any sense to me.  This is what I have parsed from what you are saying:
Red Line = Noise + Gaussian
Blue Line = Red Line + Lower Gaussian
Blue Line = Noise + Gaussian + Lower Gaussian
Blue Line = Noise
Red Line = Original
Blue Line = What you got
Clear as mud.  What you got isn't what is original.  You arbitrarily chose a spot to add a contrived Gaussian to the red line to get the blue line, yet that is what you started with.
You call the red line a gaussian + noise, but it doesn't include the gaussian you added.
Let's start with this.  Show the data set you are starting with.  The original data, the time series as you will measure it.
I'll take another look in the morning, and probably delete this answer, but it was way too long for a comment.
In the meanwhile, maybe a look at this:  Estimate peak width from a vector that is a superposition of unknown number of identical Gaussian peaks with different heights?