Is it reasonable to expect my brother to hang out with me once a month if his wife doesn't like me?

Your brother is starting his own life together with his wife so naturally he will spend less time with you. However, all couples need their own time to do what they need for themselves. Your SIL should understand if your brother wants to spend time with you and once a month is not a huge ask. I think from here it is up to your brother to have a word to his wife if he wants to spend time with you. I would have a word to your brother about it and if he doesn't do anything about it then I would move on. Ultimately this all comes down to your brother now and not your SIL.