What really struck me is that your closest friends are flying to the funeral, but your wife is not going? Perhaps one of the friends could stay with you so that your wife attends her own father's funeral.
I know what it's like to not have your spouse with you - twice. My husband had to fly 10 hours away for a week when I was 36 weeks with our first child. Thankfully, I didn't go into labour early. Our second child, he had to miss the birth and their first 3 months as he was on a tour of duty. He was actually away for a year, so literally left the day after conception (pregnancy not planned). He came home for 2 weeks R&R, which coincided with the 20 week scan. It was tough, but we just had to deal with it. It was his duty to be away, and a father's funeral is similarly important.
I only had PIL as we were living in my husband's country, so my MIL, who I didn't know very well, was with me for the birth.
Chances are that DW would be back in plenty of time to support you, so I fail to understand why you think she should miss the funeral. I understand you are worried and feeling vulnerable, but you do have other people around you who could step up in the remote possibility that you go into labour, they just aren't your preference.
If you don't give her your blessing to go, there is likely to be resentment down the line from your wife and her family.