I don't think you are being unreasonable at all..

I would be pretty furious if my DH had left to play a game.. As it was my DH left the hospital less then an hour after our dd's birth to go have Lunch with the kids.. while I knew he had to go help my mum with the 3 boys I was still hurt for Dd he had left her there alone.. Silly I know but still (I had 3 c/s first was a natural delivery)

After my first was born at 12:10am Dh and my mum left the hospital around 3:30am but Dh was back at 7 the next morning.

My sugesstion to you would be this.. Say right I understand you want to leave for your poker game but how about we wait and see how we are all doing.. Maybe you will just want to sleep so it might be ok for Dh to go to his game.. but have him promise that if you feel you need him to be there with you then he stays kwim?