If you have good stocks and the time to make it work, eg use it all efficiently, look for yellow sticker meat etc, then you might manage as it's only 4 months.
You say you've 'cut back on everything', so just to check, have a look through:
www.moneysavingexpert.com/family/money-help/
Also sign up to the weekly email. Try the tips about free money for swapping your bank account. Also look out for offers on Christmas presents.
Christmas - presents for your immediate DC only, and perhaps token (eg bottle of wine) presents between you and DH, parents etc. No presents for other adults. You can't afford to waste money exchanging tat. Stick to existing decorations for Christmas, Halloween etc. You do not need to buy anything new. Ask around if you don't have things, nearly everyone has things spare.
Can you get invited elsewhere for Christmas dinner and promise to repay the favour another year? Also, don't worry about stocking up on all the inevitable extras that will start appearing in the shops soon (Quality Street, mince pies, weird cheeses etc). Buy none, see what you/DC get for Christmas and then go and look in the sales when it's all reduced and get something then. Christmas doesn't have to be about buying mounds of extra food and then eating it all 'because it's there'. Look for other cheap things to do to make it Christmassy like going for a walk in the woods if it snows, go see the Christmas lights locally - even walk round your neighbourhood and see your neighbours decorations if you have any locally that really go to town. We have streets near us who go way overboard, the whole street festoons their entire houses with lights, they are featured on the local news and then the streets get blocked with traffic when people go to see them.
Don't worry about the comments about teens needing unlimited access to snacks and high quality protein. You can't afford to feed locusts, it's only a short term thing and you only have them EOW so they can have the bean chilli while they are with you and let their DM worry about feeding them in the Mumsnet approved manner.
Look for cheaper cuts of meat and make it part of the meal, not the focus. See if you have any markets, farm shops or butchers locally that do bulk meat packs, deals etc. We have some where if you take the £20 meat pack or whatever, there's probably £40 of meat in there if you bought it separately. Get these, freeze in meal size packs and use those to make stews, casseroles etc with lots of pulses and veg to make them go further.
Also stick to seasonal veg and the 49p specials type offers, which will be much cheaper than out of season or 'fancy' veg like asparagus, sprouting brocolli etc. Look at frozen veg. Use your freezer efficiently as this can help you save a lot of money.
Finally, the suggestion for you to try and do some work like babysitting is a good one. Put yourself out there with family, friends and even amongst your DHs ex's circle if relations are amicable. It's coming up to Christmas, so there will be party nights etc to cover and people might be more likely to trust a responsible adult than a teen. Or even try and join an agency to get work? Even a couple of evenings babysitting a month could make a huge difference, and you could get a lot more work than that nearer to Christmas if your DH will be around to look after your toddler.