Please don't do this, OP.
The lack of leave over Xmas does not sound ideal, but you should have checked this before taking the job.
As a long-term strategy, try to find a different job which allows at least a little bit of extra leave over the Xmas period, if this is important to you.
Short-term, talk to your employer if you are going to struggle with childcare over this period, and ask him or her for advice and perhaps some accommodation given your status as a LP with young children.
Taking almost a month off based on a falsehood is really piss-taking behavior, sorry, and if you get found out you will be deep in the doo-doo, and rightly so.
I think you need to ask yourself, do you need the best part of a whole month of non-working to "do Christmas" with your children anyway?
I am wondering if you have had a lot of Xmases where you did not feel very present with the kids (work, lack of money, breakup, health, if you are a lone parent of two young kids and a chronic illness, I am guessing the last few years have been tough) and have built up this kind of idealized image of Christmas in your mind, believing that if only you can spend weeks on end intensively "doing Christmas," it's going to be this absolutely incredible experience.
In reality, taking three weeks off to intensively "do Christmas" sounds like the perfect way to create a lot of really over-hyped expectations for both you and the kids; the actual Xmas stuff itself will never live up to the hype, and trying to eke out three weeks of long kiddy-centered days-out on the average parent's daily budget sounds exhausting and stressful.