See the first example of même as an adverb, I think that it's modifying "my mother" and thus is an adjective not an adverb. Now if it had said, "...my mother even went..." then it's modifying "went" and is an adverb.
Même ma mère est allée ...Craig,
my understanding is that if ‘ même ‘ was functioning as an adjective, it should be able to be replaced by other pertinent adjectives and make sense. I haven’t come up with any that really work.
On the other hand as an adverb, it should be possible to replace it with other adverbs and make sense, eg heureusement/malheureusement, which fits as far as I can tell. I think ‘ même ‘ is a whole of phrase adverb here “ even ( my mother went ) “, just as we have in English.
If même came immediately before the noun, eg ‘ les même mêres ( faire qqc) ‘ I would consider it as an adjective, but being separated from the noun by the determiner is a different situation I think.
Interested to hear other thoughts and explanations.
https://about-france.com/french/adverbs.htm
https://www.thoughtco.com/sentence-adverb-1692084
See the first example of même as an adverb, I think that it's modifying "my mother" and thus is an adjective not an adverb. Now if it had said, "...my mother even went..." then it's modifying "went" and is an adverb.
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