I'm married for the third time. In my twenties, I thought divorce only happened to other people and wouldn't affect me!
First husband had an affair with a much younger women and we divorced when my kids were 10,12 and 14. Second husband turned out to be controlling and was probably a homosexual in denial. I lost around £60,000 through my second marriage and was, with hindsight, quite depressed for a good part of the 6 years I was with him. No kids together, thankfully.
Met my third husband at work. My mum was not happy at first two choices ( although never tried to interfere), but she adored my third husband, whom I married when I was 48. We've been together around 18 years now and all the children and grandchildren love him to bits. Maybe we should all value our parents' opinions on partners more!
I think it's deciding what works for you and not feeling you have to stay single or have to find a new partner. Coming to terms with the past is a big part of it as well - not always easy as many here can testify.
If you want someone to share nice meals, concerts, walks etc with but don't want the financial/legal commitment , I'm sure there are plenty of men who would feel the same. If you're happy on your own, with no-one else to answer to, then don't feel pressurised by your children.