What coping skills can I use as an adult who has their own family?

mm... as a child and not much of an adult despite of being one. I think the most important is to listen. Try to reach out try to talk try to communicate more even if it'll be hard you're an adult why not right? Be mature and take the initiative to ask. Even if it'll be embarassing asking is what missing ths days. And yes don't ever assumed because there might be an explaination for their behaviors.

I don't like how people say "count to ten/100", and since I don't really know your main problem, I can't really specify what coping mechanism would fit you best, but I know that distracting yourself helps a whole lot, just with anything. Games, sports, activities, drawing, music, etc...

Try to spend more time with your own family and care about them because they are all you have now and love them

Don't hold on to tight. The more you push children away from something, the more they want to do it.

As an adult, I know it can be very challenging to take care of one's own family... and have something left for yourself at the end of the day. I try to journal to collect my thoughts and be able to reflect on my journey. I also try to keep in touch with friends, have coffee or even just make plans to email or chat online as frequent as possible. Perhaps having your family join you for an activity you find interesting and fun, like a book group or doing an art project at a local arts & crafts store would be a great opportunity to connect, as well as doing something meaningful.

Depends what you need to be coping with! Coping methods are not constricted to age groups or any demographic, anyone can use almost any coping method. Some good overall ones are controlled breathing, guided meditation, and progressive muscle tension/relaxation.

Being patient in moments of frustration and knowing that if I kick and scream over the small things, my kids will learn that all stress is bad too. I try to remind myself of this often.