Keep in mind this JUST ended, so it is very fresh for you.
And yes. Getting over 1 break up might be easier than getting over 2 breakups at the same time.
And yes. Getting over 2 breaks up at the same time when single? Might be easier than when married with kids.
All you can do is give yourself some grace, and just do your best.
It is ok if your "just broke up" best at this time is not the same as your "regular healthy best" of other times.
A person who broke a leg? They will do their best on crutches and so on. But they don't expect themselves to sign up for a marathon. Maybe some chair yoga and other kinds of PT while healing, but not marathons! They are not at their "regular healthy best."
So my suggestion is to keep expectations of yourself realistic.
Find ways to appropriately express your sadness/grief as you work through
the stages of grief -- journaling, talking to trusted people, taking walks, gardening, drawing, painting, reading... whatever it is you do that is a quiet, comforting activity when you have the spoons to do it.
If you don't have the spoons?
Run the dishwasher twice.
Or eat off paper plates and skip the dishwasher entirely. Do what you gotta.
Ask spouse, family, and friends for appropriate level support. Like bring over a dinner. Come help mow the lawn. Small tasks so things get done, but you also get some down time to cry, nap, etc. I saw on your other thread you are seeking counseling for extra support. That's good.
Depending on the ages of the kids, you might do some feeling cards. You don't have to deep detail WHY you are sad, but if very small? Sometimes kids connect dots wrong and blame themselves for the different vibe in the home while you heal.
If I was looking for some today
I might pick these. They suggest what one can do about the feeling. (My own kids are much older now, these weren't out when they were little. Their set just taught the feeling names and we talked about things we could do. No printed suggestions.)
Or the kids are opposite. Don't even have a clue parent has stuff going on and maybe need reminders for a little extra quiet or "going easy" on the parent. Maybe you can arrange for the kids to go away for the weekend to grandparents or similar so you can spent the weekend resting?
I am sorry you struggle right now. I hope things get better over time for you.
Galagirl