Consider relaxing some of your standards and expectations
In all likelihood, you have a long list of responsibilities, concerns, and worries. After all, you still have your previous commitments, as well as some new duties arising from your partner's diagnosis. How will you manage?
One approach is for you and your partner (when possible) to discuss what is most important to your family, and to focus on these priorities. Then purposely try to lower certain expectations and let some things slide — at least for now.
For instance, perhaps you can tolerate a messier house or fewer home-cooked meals if it gives you more time to spend with your partner and children or to take care of yourself.
Cutting back on activities that do not directly benefit your family, such as chairing the annual school fundraiser, may make your life easier. See what you can take out of your schedule. Consider taking a walk or shooting some hoops with your kids instead of attending optional job-related meetings or activities. Or maybe you can stop at the grocery store for some prepared food instead of spending time in the kitchen cooking dinner.
Both you and your children may have to accept less (or different) attention from your partner than usual
In the long run, going through a crisis such as the diagnosis of cancer may strengthen the bond between you and your ill partner. However, on a day-to-day basis, it may not be realistic to expect that your partner will be as supportive of you as usual. Your children, too, may notice and react to the fact that your partner has less time and energy for them.
With treatment, cancer patients may temporarily experience difficult side effects and a drop in energy, while also having many thoughts and feelings to sort through. If you can, talk about this with your partner and try to find ways to stay in touch. If the opportunity arises, spend time enjoying each other's company instead of finishing paperwork or mowing the lawn. Share quiet activities when your partner is not feeling well, and make the most of good days or weeks. Look for ways to involve the kids as well. Maybe you can pack a picnic dinner and spend a pleasant evening together in the local park. If you've all had a stressful day, maybe you'd rather watch a favorite movie and snuggle on the couch with your children and partner.