My condolences on your loss.

I'm going to try to work through all the considerations you should make, as you are contemplating allowing your father back into your life. i'm going to ask you to evaluate and question your past experiences with your father. Because we assume a context of abuse in this community, I want anyone reading this to know I am not questioning whether OP was abused. OP is questioning whether to let an abuser back into his life, and at an especially vulnerable moment. Whether or not OP should allow this to happen at all, and especially right now, is what we're trying to figure out. Now, on to my response.

My biggest concern is the timing. Since your maternal aunt has obviously been feeding information about your life to your father likely for the entire time you were NC with him, I wonder why he waited until now. The news that you were going to be a father would have been a perfect (and more pleasant) time to make a gesture of good will toward reestablishing the relationship between you. Of course, new fathers are also highly protective of their families. You weren't vulnerable then.

Look at the chain of events. Your maternal aunt shared information about your life to someone you chose to cut off. She also gave your wife's phone number to your father, someone they may have viewed as being even more vulnerable than you after what just happened. Then your paternal aunt called without invitation and under false pretense. Next, your father called without warning or invitation immediately afterward. Their timing implies they wished to take advantage of your vulnerability after the tragic loss of your son. Of course, anyone who just lost a child would instinctively want to speak with their father at a time like that. Not their actual father, but the proverbial one. The one we all wish we had. My own father horribly abused me and, at one point, tried to attack my pregnant wife. Sometimes, I pine for a father I could turn to when my life is rough and consider contacting him despite being NC for years now.

So you spoke with him on his terms at a time when your judgement is clouded. Now, he's coming to your son's funeral, and behaving as though the lines of communication are open. I am sure you did not make the decision to go NC lightly. So let's examine your relationship with your father prior to NC and how closely he resembles the picture of a narcissist the links in our sidebar illustrate.

You say he was neglectful to the point where it constituted abuse after your mother died. I want to ask you a question here which is solely for the purpose of helping you evaluate whether or not renewing contact is a good idea. In your opinion, was his neglect of you and your sibling solely due to the loss of your mother? What I want you to determine is if the neglect (which I don't doubt for a moment was abuse) was the extent of the abuse. If so, he may have merely withdrawn emotionally in response to losing his wife with the result being that you suffered having a shitty dad who would have otherwise been a decent father. That's a tough consideration to make. You should take your time.

If, however, the descriptions of narcissistic parents fit your father, then you need to understand that your father has not likely changed at all. In fact, his timing could be construed as continuation of his narcissistic abuse. He's being manipulative. He'll love bomb you long enough for you to let your guard down then he'll start treating you just as abusively as he always did.

This is a difficult situation. Dealing with this should not be your focus right now. You should focus on your wife and on your own grieving process. If you are not already, please see a therapist. Perhaps both couples therapy and alone. Bring up the situation with your father.

tl;dr, my bottom line suggestion is to only allow him to the funeral if you truly want him there, and to tell him you will not be reconsidering where your relationship with him stands until after you are done grieving for your son. That you will be the one determining how long that will be, not him. If he bristles at these boundaries, you likely should not let him back into your life. If he steps out of line in how he interacts with you at all from this point until you make your decision about your relationship with him, cut him off again. Oh, and make sure he knows not to contact your wife in any way for any reason without your express permission. She does not need to deal with a potentially highly manipulative abuser trying to take advantage of her vulnerability, either.