I am not a pundit in grammar but here are my opinions; 1. I want to now, at all cost, what her mom wanted to say to my father last week. (Note the commas) For second, third and fourth sentences, there is just no need to use "just".
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For adverb positions, see here: http://linguapress.com/grammar/word-order.htm
For split infinitives see here: http://linguapress.com/grammar/points/split-infinitives.htm