I know how ~がる constructions work in reference to subjects in the third person. However, I am a bit lost in regards to which situations necessitate the use of ~がる with the first person.
For example this sentence is correct:
私がアイスクリームを食べたがると、母が食べさせてくれた。
But this sentence is wrong
私がアイスクリームを食べたいと、母が食べさせてくれた。
I don't know why.
Upon conducting some google searches in an attempt to find the answer to this question, I found a source saying that one can use ~がる with the first person to narrate something that happened to them in a detached manner. Interesting but not really relevant to this particular distinction, I think. Or is it?
This paper also mentions the existence of the first person ~がる construction, but I'm pretty sure it doesn't say anything helpful (but I could have overlooked something).
Does anyone specifically know why 食べたがる MUST be used in the above sentences?