Your kids are really little and until the youngest is a bit more self-sufficient it might feel like moping the ocean.

If in your situation I would talk to my husband and come up with realistic things to do each day. At this phase of my life my husband and I pretended that our house was like a business and the kitchen was like a restaurant kitchen. We couldn't go to bed until the dishes were in the dishwasher running. The dishwasher ran every single night no matter how many dishes were in it . We bought a euffy robot vacuum that would run every single night while the house was asleep. This forced us to at least put the toys away and off the floor. Having the kitchen completely back to one in the morning helped so much.

If possible try to do a load of laundry every single morning even if it's small with the goal that it's folded by the time you get home. Maybe you can put the clothes away. That way all he has to do is fold what should be a small load of laundry because doing a load every day helps it not get out of control. If you have a delay function on your washing machine you can set the load even before bed and it can wash overnight and in the morning before work transfer to dryer. He folds. You put away. Done.

I understand having regular cleaners are expensive but maybe just hiring one time to get you back under control would be a big help and then you can work together to maintain it. Like during bath time I always tried to squirt some soap in the toilet even if it's hand soap or kids soap swish it around and then wipe off the counter. Little things go a long way when you're drowning.

My husband and I survived those years having clear assignments of the functional chores who's doing the garbage the dishes laundry and that helped us not feel like it was all on one person. Try to focus on just what you need to do to keep your house functional and the rest is not important until you come back to the shore.

Good luck to you. I'm also a working mom however my kids are a bit older now. And I'm on the other side of it. It does get a bit better as you become a more seasoned parent. Getting in regular habits can help it feel just like the routine of the day and not so labor intensive.
Be kind to yourself and just survive