Your response is fine. I'm like you, if I make plans I expect to attend them & I've had guys set something as far in advance as 2 weeks, which I keep. I mean how hard is setting a calendar alert...
Granted life can happen while we're making plans, and people could meet someone they prefer at any time so...
She's experienced and may expect an occasional touch base text so she knows you didn't blow her off; and let's face it a touch base text takes all of 30 seconds and lets her know you didn't forget about her, especially if she needs to hire a sitter or make other babysitting arrangements to accommodate a date. Few things are more annoying than paying a sitter or going to other preparations and not being sure your date will show up. So a confirmation of some sort can be a good thing and is not a "beta" move.
Just say "Hope you are having a good week, see ya Sat" or if you think that's weak then "Headed to a meeting, hope you're having a good week".
Neither of those communications take any time at all, they don't invite a response (if she gives one fine but don't get into long convos), and either one keeps her advised she is on the radar.
You have been at this long enough to know that
women with kids are not as untethered as childless women, people are flaky, and a text such as the examples I gave are not "beta" in any way.
Sometimes a guy with lots of options puts off the player vibe (which good for you - you have many options and a robust dating calendar), and 1. women either want to compete for a man like that, or 2. are put off by it, or 3. at least understand it so they don't over invest/have expectations beyond what you do.
She sounds like she is #3 (which is the most pragmatic mindset), but that she does like you.
So no harm no foul. See her Weds (Send her a sh!tty funny text Tuesday afternoon that says "Hey you...you have a date tomorrow BTW") I think that keeps her anticipating things and keeps it light, and busts her chops just a bit too.
Good text game is light, fun & sparse, but it does also let her know you didn't evaporate.
Sorry so long! Cheers!