How can we handle long-standing religious traditions in our extended families when our own family and children don't follow any religions and don't have any gods?
An especially difficult issue for godless parents raising their children without religion can be dealing with the religious traditions in their extended families. If the parents themselves were raised without gods and religion, this probably isn't an issue, but most do come from at least marginally religious families which have a few religious traditions, even if it's merely to attend religious worship services on major holidays. The more devout a family is, the more difficult it may be to exclude not only yourselves, but also your children from the traditions.
Traditions can be very important for families because they create a sense of connection and continuity from one generation to the next. When, for example, people sit down to Thanksgiving dinner with their children, just as they did as children with their own parents and their parents did with their grandparents, they experience a connection to those earlier generations and feel like there's a continuity that stretches across time.
All of this is even stronger with religious traditions because in addition to creating a connection to earlier generations in the same family, religious traditions create connections to the broader religious community past, present, and future. When people go to church on a religious holiday, just like their parents, grandparents, friends, and neighbors, they experience a connection to their religious community that transcends their own lives.
Because of this, continuing family traditions, even religious ones, often isn't perceived by participants as just being about religion or theism. It might be bad enough that one has rejected their family's religion and is raising their children not to believe, but rejecting family traditions seems to cut even deeper and is perceived as a rejection of the family itself. Ending traditions that are thought of as extending back through the generations is seen as a blow to the family itself because the connections from one generation to the next are severed. It's no wonder that many atheists experience a desire to keep up even those traditions which are ostensibly "religious," despite not believing in any of the religious content.
This is an understandable position and there are good reasons to try as hard as possible to work out some sort of compromise. If you are raising your children without gods or religion, it would be hypocritical to participate in religious rituals as if you were believers; however, being godless is not itself a reason to dismiss all traditions entirely, even those which might have religious origins. This would exclude attending religious worship services, of course, but it shouldn't exclude traditions like sharing special meals, spending time together, or even perhaps singing songs like Christmas carols.
It's also worth thinking about creating new traditions or simply modifying older ones so that everyone can participate comfortably. Instead of attending religious services on a holiday, for example, the family might find something else to do together, such as attending a play or doing charity work. It will be important to help religious relatives understand that while you can no longer participate in the same religious traditions as they do, this doesn't mean that you don't value the way common traditions can bring the family together. It will be incumbent upon you, however, to take a lead role in developing such traditions and rituals that will bring people together.
Actively participating in traditions like these with your children means spending quality time not just with them, but with other relatives as well. Thus the connection which is created between you, your children, and your relatives is not imaginary: it exists because of the shared experiences and the knowledge that, even when you're apart, your engaging in similar activities which bring back memories of the shared experiences from the past.
Some people may fear that raising one's children to be godless might cause them to fail to appreciate family and traditions. This could certainly happen if godless parents don't make the effort to prevent it. Religious believers don't need to take extra steps because they can simply fall back on traditional religious rituals to achieve these goals. Irreligious atheists don't have this to fall back on, so must remain conscious of what they are doing.
Some may conclude from this that godless parents are at a disadvantage, but being forced to remain conscious of what they are doing and what they need to do is actually a positive advantage. Relying on traditional religious rituals may only encourage lazy parenting because people don't have to stop and think about what they are doing. Irreligious atheists who are raising children will have to stop and think, which will hopefully help them to reach better decisions.