Hell no. Do not tell them. You're a part-time freelancer!
I've been a freelancer since before my kids were born (although rarely part time). With both, and both with fairly harrowing EMCSes, and one very needy baby and one absolute angel, I was still able to check email, do a few bits within a couple of weeks. Sure, housework wasn't a priority, and I stopped making ex packed lunches, but it really wasn't an issue (DS1 even joined me at a few meetings!)
My kids are fantastic, well behaved, well liked, well loved, despite ex basically leaving me to raise them (and I thank my lucky stars I kept up the freelancing, despite him encouraging me to give it up, so I could end the relationship when it became clear what he'd been up to|)
They are well used to me occasionally having to close the door and go on a call (and they're not scared, they'll gently open the door, establish if I can chat, before asking for a snack for instance - very reasonable kids).
Being freelance (also remote) means that I have mitigated the risk of losing my career, but I can still take them to school/pick them up, go to sportsday etc. and generally be the present parent they need (I could make a dig about their father here, and I will, since he's a lazy coward who doesn't deserve the wonderful kids they are, and he sees once a week!)