As far as I have ever been concerned, no gifts are EVER required. There are occassions we normally gift for, but a gift is a gesture and when things are tight, family always comes first.
Your children and immediate family are priorities, being reasonable on a tight budget. If your husband doesn't mind, do something small, homemade, or cheap for Father's Day. I would rather meet my family's needs than have a gift myself.
Do not give gifts for something you are not invited to if you cannot afford to do so. So many people came to my wedding who did not send gifts, and many (most, in fact) who were invited and did not come did not even send cards. Cards are a polite gesture, and courteous people will have no other expectations.
We had many friends in college whose gift to us was to be able to come to our wedding. You can adjust your gifting because of your finances and should not have to justify yourself. If you are close to these friends, you could always say in a neutral situation, "I wish I could offer so-and-so a gift, but things are so rough for everyone right now." I have done that because of holidays we could not give general gifts for (just immediate family and our kids) or friends' children's birthdays, etc. If there is no money for it, there is no money for it. Your family's needs are more important, and your children can always make something homemade.
My favorite wedding card was from some of our friends who were newly married, recent grads. It was homemade and adorable and totally reflected their personalities. The back "made by" company name was something like, "Feed the starving college graduates company." Cute, clever, and we were just excited they could come.