Elizabeth Woodville completely throws out Edward IV's will, violates Richard's rights under that will wholesale, loses English territory, conspires with Henry Tudor...then takes Richard's wife and son hostage and demands a ransom during which Anne Neville suddenly. If you can't see why this would look bad...
Especially considering that she is doing this out in the open. As in, everyone can see what she is doing, and they are all acting too stupid to actually do something about it.
Every single old blood royal descendant, such as the Buckingham's, Northumberlands, Norfolks and even the remaining Neville's can see this. They would literally rally around Richard and would present a threat to the Queen. Hell, they should actually be doing this, regardless of what the position that the Queen occupies. Disregarding the will is an absolute no-no. She would be crucified for that.
Elizabeth also makes it obviosu that she is out to get Richard by literally
protecting the person who
kidnapped Anne Neville. She makes no secret of it, and practically gloats it around court. Again, this would rally all the other nobles around Richard.
And lets not forget that she literally "invites" Richard to get his wife and son back. "Invites" him. He should have shown up with an army to get his son back, to prove a point to the upstart Queen. He is not taking her shit.
By the time you get to where the reconciliation is Richard should have revolted and all of the other magnates/nobles in the land would have practically joined him against the queen, seeing as how she had treated Richard.
Her attempts to secure an alliance with Henry Tudor. Not a bad idea. But, the fact that Henry actually submitted to the offer, and again, it was out in the open, especially if the French King knew, it would not be long before the English population knew. Of course, this is a good thing, being that it does offer a temporary relief of pressure, but the Queen is not acting with the consent of the nobility, or at least, Richard - who is the most powerful magnate in the land at that time - and is supposed to be the Lord Protector.