Plane Travel Internationally - Change of plans for ticketing/check-in?

I booked non-refundable/non-changeable plane tickets to Mexico next month for myself, wife, and infant child. An emergency family situation came up and my wife went with our child to Mexico in advance since I cannot take off work in the US. She will stay there the entire time with my child and the plan is I will go to Mexico by myself in May and we all return together on the same flight reservation.

My main concern is when I go and travel alone for the departure flight, is it ok to just check myself in to travel while my wife and child are absent? My child is listed as Infant in Seat under my name specifically if that matters. Also, is the return flight also affected now if all 3 of us plan to return together? Will I have to book a separate flight again for my wife and child since they missed the departure check-in?

I appreciate any help on this! Thanks!