I've separated from my DH 6 years ago. I'll start with the negative;
The effect on my DCs. My ex was fine until I met my DP - then holy hell broke loose. The poison fed into their little brains was so harmful - one DC refuses to go to his home and it has caused him a lot of inner turmoil over the years.
The positives;
I didn't have a pot to pi$$ in but I made things happen.
I changed career and this has enabled me to stay in the family home with him off the mortgage - that feeling was AMAZING. I kept walking around my home (that I had lived in for years) with the biggest feeling of accomplishment ever.
I went on a sexual voyage of discovery. Realised what I wanted and had so many experiences. 
I met my DP after 3 years of being single. He was my second date from OLD. He is everything I ever wanted but didn't know a guy like that could even exist. My DCs love him, respect him and take their lead from him due to his level-headedness. Hes good for them. I was concerned that nobody would love my DCs as much as I wanted them to and he does. We are moving in together to a beautiful home next year.
The time without my DCs. This was easier when they would both stay with their DF but we still get time. That time on my own and with my DP is much needed and priceless. Planning something with someone I want to do things with had given me so much more energy to make things happen.
Celebrate your victories OP, however small. Just knowing that you've accomplished a good life for you and your DCs is just the best feeling in the world.
Good luck