It could, but not necessarily. Caffeine affects different people differently. Have you always had tea/coffee like you do now? If so, you might have already developed some degree of tolerance to it, so I don't think caffeine is likely to be the cause of your symptoms. On the other hand, it could have begun to affect you that way even if you were accustomed to it. I'd suggest trying to stop consuming caffeine for a while to see what happens. Might have something to do with your diet, too. And stress might be an important factor as well; taking care of three kids, working and maintaining a good relationship with your husband simultaneously must be difficult.
Hello and hope you are doing well.
Its unlikely that caffeine could have that effect of waking up early. But you could still avoid it in the evenings or night time. Try not to nap and try to sleep later and see if your symptoms improve. Also, exercise in the daytime, this promotes good sleep.
Hope this helped and do keep us posted.