I thought I could offer my two cents here as an "old mother," opposed to you youngsters. :-)
Also, my Dad had his midlife crisis when my brother was a newborn. The OW actually gave my mom the outfit we brought my lil bro home in. We, at that point, had NO idea. I watched my brother grow up with OW. My dad left when he was an infant.
Anyway, the parenting the OW will do isn't real parenting. They get the weekend parenting.
When your girls say, "I hate YOU! You've ruined my life" (AND THEY WILL LOL), WELL, that's the real parenting.
When you realize that the "friend" who sits on the bus with them is telling them about blow jobs...that's the real parenting.
When they want to wear the latest in SlutWear to the school dance, that's real parenting.
My dad and OW did a lot of weekend parenting. To this day, they don't know the day-to-day details of life for my brother. My mom does. My mom knows that my SIL recently had a miscarriage. My mom knows how stressed by brother was when his inlaws had financial issues. These are the details a MOM knows.
OW will never replace you. I promise. They will grow to care for her like they do an aunt. But, YOU will ALWAYS be the MOM.
Women who are comfortable becoming a third wheel in a marriage/family are not, IMH, able to have deep and meaningful relationships with anyone, let alone children. It's easy when they are little...just wait.
The next time they freak out at you because you "Ruined MY LIFE!" know they only do that because they feel safe. They will give you all the nasty because you are the mom.
It's a huge burden as a single mom...but, that's the payoff for being truly, genuinely THERE for them. And, they will appreciate it...eventually.
And, you guys are doing the grunt work right now since they are little. I remember how exhausting it is. Even with Smokey living here, I was very alone.
But, the consistency and effort you put in now, it does pay off. Funny thing, you will forget the little stuff that you did when you didn't feel like you had anymore energy...they won't. My D20 reminds me constantly of stuff I completely forgot. Stuff that meant the world to her.
"Mom, remember when I collapsed on the soccer field because I couldn't do one more 180 and I started crying? You were there urging me to get up."
"Mom, remember when you forced me to actually drive 1000 hours before I was allowed to take my driving test? I hated you for that, but, I appreciate it now."
It's the in-the-trenches stuff they appreciate later on. For reals.
"You know, it's times like these when I realize what a superhero I am." Tony Stark/Iron Man
“Focus on what you can do, then do it with all your heart.” Lois Wilson