Question / Help Gaming pc set up

I just want to understand an know how this set up will work...
I want to start streaming with a duel PC set up.
My gaming PC is running on i7-8700k, msi 1080ti, and 16GB Ram.
the streaming PC i s a laptop but i know it is capable to run the stream.
my issue is with the gaming PC sine i am going to plug a capture card in the HDMI port and the DP to my mine monitor, the issue rises hear i want to record my game footage on my PC at the same time so i can post it on my YouTube channel with out the sounds of notifications.
is it possible or not and if it is not possible what should i change or add so i can do that.. is an extra GPU needed?