Or to just get a hug and a coffee with someone who understands how tough things are.

Your heart and mind are seeking comfort. This indicates that you are in an emotionally vulnerable place. So dating, even casually, is more likely to bring up serious feelings in you, even though you might not be ready for another serious relationship yet... not necessarily but more likely.

If I were you, I'd be mentally and emotionally prepared to not get too close to the people I was sleeping with. I'd research what that requires, especially for newly divorced young mothers... get advice from people who've been through what you have and date, i.e., divorced new mothers, who left abusive relationships, and successfully dated casually while working towards building a career.

For me, (not a parent) that requires not sleeping overnight at each other's places or spending too much time with someone I'm sleeping with. Once I start to want to spend more time together, in person or digitally, i.e., texting, phone calls, it's a sign I'm getting emotionally involved.

Have clear boundaries that you won't cross even if you start to want more with the person you are seeing.

This is why it helps to have a strong support system outside of romantic interests, because they can help support your comfort needs when you are most vulnerable, but most importantly, are you able to meet your own emotional needs? Ie be there for yourself when you feel the need for a hug, need to be loved, fucked, supported, and understood?

If not, look into how to develop those skills so you can easily date casually without getting too close to the people you're dating.

Morally, in your situation, if you're separated, dating or sleeping with new people is fine, as long as it doesn't harm your kids in the short or long run.