OP, do you struggle a bit with keeping on top of life in general?
Because you seem to see things that I see as complete non-events as big, big tasks, and that might be affecting your mindset.
So feeding yourself and your child breakfast and lunch - meh - no biggie - I certainly wouldn't see that as "catering two meals". It's bunging some cereal in a bowl each and making a sandwich each or similar - something that most people do daily without even blinking, probably takes a total of 10 minutes including tidy up afterwards, but seems a big, big task for you.
Equally, cooking an evening meal and washing up after - most people do that daily, and don't think about it - it's just an integral part of daily life. And if you're talking about inviting an extra person along to regular family meals (like roasts or a pasta dish or a simply chilli or curry etc) then really all they are adding to the mix is an extra plate and an extra knife and fork, and it's hard to see why that's significantly different to the standard cook and clear up after dinner that everyone (presumably including you) does daily.
And again - the whole tidying up before they come? Assuming your house is generally tidy and functional then why does someone coming round to share a meal necessitate anything different to the norm?
If you are talking about throwing major dinner parties - planning a menu with starters, mains and desserts that you wouldn't ordinarily make, all cooked from scratch. Sourcing obscure ingredients. Researching which wines complement your dishes. Laying the table with the best crockery and cutlery, washing and ironing the tablecloth and napkins. Sorting out floristry and table decorations etc, small talk with people you don't know awfully well etc- well yes, you have a point, that kind of thing is hard work. But I don't really think many people do that kind of "dinner party" anymore, and I'd certainly say it's not really appropriate for a single mum of a 5 year old to try to host if it's not something they actively enjoy doing.
But actually, I get the impression it's more that you want (for your benefit) to ask someone you know well (family or friends) along from time to time to join you for your everyday meals that you'd presumably be cooking anyway. And in those circumstances, I'd just crack on exactly as if they weren't there, but just lay an extra place at the table. Which would include not tidying up beyond the regular tidying, and just stacking the dishwasher after dinner as I would normally do. I wouldn't expect the guests to suddenly start doing my washing up for me, but I guess I'd expect them to either be chatting to you in the kitchen whilst you cleared (and probably pitching in in a minor way - passing you this and that for example), or otherwise chatting with your child in the the other room whilst you tidied up.