In this following sentence,
which one is better:
whatever she said, I will/would insist on doing that tomorrow.(now I'm speaking)
Because we can just use "would" in the following sentence right?
After he finished this, he would clean the floor.
Thanks in advance
Whatever she said, I will/would insist on doing that tomorrow.
What the sentence means is ambiguous; there is no way of determining which modal is "better" without more context.
I can think of at least seven different things your sentence might mean, depending on whether would has a past-tense or an irrealis sense, on whether it is the "doing" or the "insisting" which is occur tomorrow, and on whether that refers to whatever she said or to something outside the sentence:
I intend to insist on doing whatever she wants, once I find out what she said that is ... This calls for will.
She said many things on many different occasions last week; my response on each occasion was to insist on doing X tomorrow ... This calls for would.
I recommend that you insist on doing tomorrow whatever it is she told you to do ... This calls for would.
I made up my mind beforehand that regardless of what she might say at the scheduled meeting, I was going to insist on doing X tomorrow ... This calls for would.
I am wholly indifferent to what she said yesterday; I am determined to insist on doing X tomorrow ... This calls for will.
The strategy I recommend when you meet with her, the strategy I would adopt, is that of insisting on doing X tomorrow regardless of what she says ... This calls for would.
There are more possibilities than these; for instance, there are probably versions in which will/would has a volitive sense rather than the futurive and habitual senses illustrated here.
