1)
What were her reasons for refusing?
1.
Malbim: The action is improper due to (a) her honor - "Ana Olich Es Cherpasi", (b) his honor - "v'Atah Tihyeh k'Achad ha'Nevalim". (c) And you can marry me b'Heter - "Daber Na El ha'Melech"!
2)
Why would David permit him to marry his sister?
1.
Rashi: She was permitted to him, for she was conceived when her mother (an Eshes Yefas To'ar) was a Nochris. A child from a Nochris is not considered one's child (so Tamar was not considered his sister).
