It sounds like there are two different issues here – cleaning and food. I don’t know how many kids you have or how old they are, where you live or what the shopping is like, or what your financial situation is, so these may not all work for you, but hopefully you can get some ideas.
About the cleaning and toys … Maybe you can lock up some of the messier toys? Invest in some bins to corral the clutter? Buy the kids special Shabbos toys to encourage them not to use the messy ones? Teach the kids to clean up after themselves? Maybe others in the family can help with some of the housekeeping throughout the week?
About the food … Can you buy some of the food, like maybe cakes and salads? Can you cook and freeze? For example, I’ll make a big pot of soup once a month then freeze it in smaller containers. The weeks I defrost, I cook some vegetables in salted water then add them to the soup. Do you have access to cheap paper goods? Can anyone in your family help with the cooking or serving?
You aren’t doing anyone any favors by being a shmatta! If all else fails, lower your standards. Tell yourself that you will not get upset about the toys or whatever because there’s nothing you can do about it right now so stressing will not help. When you and your family are at a different stage, you can change things.
Hatzlacha rabba in finding your oneg Shabbos!