OP this man will ruin your life, and your DC's life.
That is much, much worse than weathering any 'embarassment' at telling your parents and friedns what is REALLY going on.
And... it wouldn't be embarrassment for you. Only for him, and sympathy and support and admiration for you having had to struggle and then having the courage to take your kids out of it.
You would NOT be 'stuck' at your parents. You would be free. You would be able to have peace and quiet and support for your birth, take some time to regroup, save some money, and eventually move out to a home where you know what money you have, you can budget and you aren't waiting for a useless nasty alcoholic to stuff it all up every time. No, it wouldn't be a bed of roses but it will be a MILLION times better than the hell you are stuck in now, especially as that hell is only going to get worse. Leaving, even at its toughest, even if you end up stuck with your parents for a year or more is at least the start of a road to a better life without this shithead dragging you down.
If he's working full time, you go to CSA and put a claim in.
He will eventually be drinking every day. He will eventually ruin his health. By the time he gets to that point, your children will be damaged by having grown up with a raging alkie in the house, as their dad. Don't do it to them.
Christmas isn't really that important - it can be special with a paper hat and a biscuit if you feel safe and happy. Please, please tell your parents what is happening and get out of there in time to prepare for your birth and take your dd away from this horrible way to live.