What shall I do?

Oh and I've told my husband if I go first I don't want him to be alone and sad.

My first husband died in 2007
Met my current husband in 2014, married in 2016.

Please meet them and be pleasant.
Life is too short to be alone and unhappy

I can see why you are upset. I would be too, but I think you will just have to grin and bear it. We can never understand how bereaved people feel unless we have the same experience ourselves, and even then, our way of dealing with it may be different from theirs.
If you want to stay in contact with this man, you are going to have to accept the way he is choosing to move on. The alternative would be to cut ties altogether, and you might regret that.
Give it some careful thought.

You have to move on now life is too short also your cousin would want him to settle.

Thank you both for replying. No he isn’t staying with us. They’re in a hotel seeing the sights as he put it.

I expect you’re both right and we will have to go along with it. It just feels wrong and disloyal to my cousin somehow. We were all very close and she suffered quite a bit with her illness. He’s always had an eye for the ladies but we didn’t expect this so soon. Also, at his age, I suppose we all thought it was unlikely to happen so fast.

Thanks for your answers, it’s good to get an outside perspective rather than just family.

I can see very well why you’re reluctant, but If it’s just a meet-up for lunch or dinner, I’d glue a plastic smile on, and go along with it. I’m assuming he’s not asking for the pair of them to stay with you?

I’d swallow my own feelings about it, and agree to meet her. Many men just can’t cope with being alone, and enter into new relationships within weeks or months of their wife’s death. It doesn’t mean that he’s forgotten your cousin, loves her less than he did, or doesn’t still mourn her.