Also the idea of Richard marrying her to Edward and remaining Lord Protector is interesting but unless she has an unusually large impact on Edward, I think Edward will remain strongly pro-Woodville (especially if Richard has arrested Rivers, Grey and Vaughan as he did OTL)
Edward is 13 years old; his political preferences really don't matter. Richard chops all the Woodvilles, and unless Edward was really fond of one or more of them, he won't care that much.
By the time he reaches his majority, it will be old news.
As to the marriage of Edward with Richard's daughter - she'd only be 10 years old. The actual marriage would have to be postponed for a few years. One question is whether he can make Edward submit when he's say 16. If he does, he's locked into a very powerful position for quite a while, barring a Lancastrian comeback or the death of Edward or his daughter.
When Edward does reach majority, he will start to rebel against Richard. The Queen may take either side. Richard's wife Anne could be a factor, too, if she does not die, and also the Queen Mother Elizabeth. She'll be disgruntled over the liquidation of her brother and son. Once Edward reaches majority, she'll make a comeback.
I think Richard could foresee this. Unless he thinks he can absolutely dominate Edward, he's going to want the crown for himself. Alternately, if he's ruthless enough, he could wait until Edward and his daughter have a child, and then dispose of Edward - thus securing his regency for another 18 years.