A Love Triangle

In the first act, I was hesitant to believe that King Edward and Gaveston are engaged in a sexual relationship, but now after reading:

"With letters to our lady from the King,
And as she read, she smiled, which makes me think
It is about her lover Gaveston" (Act I, i, 20-22),

I am even more confused than I was before. After reading this, I thought that perhaps Spencer Jr. had been mislead to believe that the King's niece was involved with Gaveston, but from II,i, 69 she mentions her "marriage day" to Gaveston. The King also expresses excitement and happiness of the wedding of Gaveston and his niece,

"And, Gaveston, think that I love thee well
To wed thee to our niece, the only heir" (Act II, ii, 257-258)

which makes me believe that his relationship with Gaveston is simply a very strong friendship that is frowned upon by Edward's supporters because of Gaveston's status. However, maybe the King is delighted about the marriage because Gaveston will be marrying into the family, and interaction between Gaveston and himself will not be suspicious or frowned upon because of their families joining.