Think it depends on how you were raised and what your values are.
Were you in a 'family is the most important' kind of setup? Was getting married or having children considered a big goal in life/ an achievement? Lots of weddings etc, lots of your parents' time spent with family or significant other?
I feel lke this is where these kinds of feelings come from. I wasn't raised with these values and finding it really hard to relate to thinking being in a relationship and having a family is the main goal in life.
Secondly, at your age it's hormones. Mid-30s is a very 'broody' or just horny time in most women's lives, prime time to be completing the family etc. Therefore your hormones will likely be driving your feelings a lot. Me and my friends certainly all felt 'different' say 32-25, priotitising wanting to be with someone etc. Also, it's hard to be a single parent with young kids, and the idyllic idea of some help and even extra income, someone giving you love and attention, may seem appealing. It may feel like you are looking after your kids 24/7, but who is looking after you?
You can go in 2 directions from here. If you want to continue being a 'family' person, put effort into meeting people.
Or look deeper inside yourself and think what else you can give to the world and wider community than being someone's partner? What are your passions, strengths, interests? How do you want to make the world a better place for all of us, a better place for your children to grow up in? Find that 'point' in life that isn't another person. Another person is rarely a solution to internal lack of purpose and emptiness.
Hope it works out for you and you find a 'point', wherever it may lie! And make sure you take time to look after yourself and love yourself while the vacancy for a partner remains open.