I'm a tiny bit confused, OP, would you like a partner or a relationship or not?
One good thing about recent times is that people who are single (or single parents, the hardest job) are no longer as stigmatised. Everyone is about being single, loving yourself, keeping your peace and all. The bad side is that for many people, having a loving partnership is fundamental about how they'd like to live their lives. I have never felt so lonely as when my partner died, even after being single all my twenties.
If you are a single parent, it's relentless and I agree, feeling on your own on a Sunday night when the kids are playing up and you've already seen a friend, it's just a lot for one person.
I don't know the solution for you, I don't know your circumstances, but there's nothing wrong with wanting a strong bond with one person to live the quieter and harder and everyday bits of life. Not everyone wants that, but most people do pair-bond, and do so even with quite unsuitable people, so don't beat yourself up for wanting human care and contact.