I can appreciate that this has been a surprise/shock to you and your sister. However uncomfortable it makes you both feel, their relationship is NOT incest and is completely legal. As they both already have 2 children each, is it likely that they would want more children together? If they do, they could get genetic testing done beforehand to minimise any risks. It is their decision to make.
Presumably, you love your brother and would want to see him happy with a new partner after going through a divorce? Ditto for your cousin. Think of the positives. You will not have to go through all the awkward stage of getting to know and like a new girlfriend, because well.....she already knows and loves your family. Similarly, their children will not have to go through the sometimes traumatic process of seeing their parent with a new, unfamiliar partner. It will be someone that they already know and love.
I have a good friend who is in exactly your situation. In his mid-40's he suddenly developed feelings for his cousin and they were reciprocated. She had 3 young teenage kids from a previous marriage, and he has a 11 year old son. He knew and loved her kids already and vice versa. They have been living together extremely happily for the last 2 years and her kids think it's wonderful that he has moved in (they call him 'Uncle)'. Like you, his family were a little shocked at first (more because it was unexpected, rather than because they thought it wrong). 2 years down the line, everyone is used to their relationship and well.....they were all family to begin with, so it has been very easy for everyone to get along.
You need to be careful that you and your sister do not encourage each other into taking any rash action that you might later regret such as cutting your bother/cousin off and causing a family rift that may be hard to mend. Are you more bothered by the fact that your brother did not tell you about it for 3 months and then chose to announce it on Facebook? It sounds like he expected opposition and is on the defensive.
Your objections seem to be worries about 'what will other people say'. In my experience, 'other people' will take their cue from you. If they ask you about it and you cheerfully answer that you were a bit surprised at the news, but could not be more delighted that 2 people you already love are now together, it will nip any possible cattiness in the bud. Why do you assume your mother is 'in denial' because she does not agree with you and is accepting of their relationship? Perhaps she can see that her son and niece are actually very well suited!
You can be honest with your brother and say that you were a little shocked at the news, partly because he has initially kept it secret; and that you also wish he had spoken to you about it before announcing it on Facebook. Be loving sisters/cousins and wish them both well, even if you have reservations. It is not worth disrupting both sides of your family over this.