Hello,
I was facing what seems to be a similar problem some days ago when trying to estimate the parameters of two linear laws mixed in the same dataset.
I managed to get some good results by using a NormalMixture as likelihood. My understanding is that a simple Normal law will not be able to capture the bimodality of the data distribution as it is only a single mode.
For parameterization, I have followed the first one given in this post.
I hope this can help.