I'm in a very similar position OP. dd1 in y1, dd2 reception, dd3 is 2 and dd4 12 months. The homework is driving me nuts. Reception is ok, two readers a week, but y1 has a homework sheet every week - writing, numeracy, phonics and a picture. Then a homework project on top of that that must be presented to the class every fortnight (6 yrs old, ffs!). Don't get me wrong, I love to do homework with my kids, but I want it to be enjoyable, not a pressure for me and a pressure for my daughters. Dd1 is a bit like me and doesn't sleep in, so while in reception, she would get up early and we would read for about half an hour every morning. However, dd2 is a sleeper, and I struggle to get the time to read with her. She is also less engaged, and it is hard to motivate her. I feel like I am letting her down, but dd4 is becoming quite a handful, and it is difficult to fine quiet time. Dh can help out on the weekend, but the dcs are more interested in playing with daddy on the weekend than doing homework.
With regards to half-term, I feel I have got it a bit more under control (well, we are only two days in here). I do tend to do a lot of day trips with all four, but I usually do it with other parents. Or play dates at ours. I actually try to 'catch up' on play dates during the holidays, as I don't do many during term time, just too difficult. We live in london, so lots of museums etc close, I usually am able to find someone to come along with us.it is, as mentioned upthread, a lot easier with company. However, everyone will have only one or two kids and different age gaps, so sometimes that causes problems with kids dynamics etc. Half terms are easier to fill with only five days. Summer is a lot more difficult.
I have to say I find that I am pushing myself to the limit each and every day. Physically, just carrying one,sometimes two children. Meeting all their needs and demands. Dh is working shocking hours at the moment, and I am finding it relentless. Yesterday dd3 had a friend over with her mum. She said having 4dds looked idyllic in many ways, and while it is, I made it look easy, if that makes sense. Holding dd3 while making pizza for lunch, running upstairs sorting out arguments between dds. Just non stop. Dd4 still waking frequently through the night. I love it, but it is relentless....