I'm not single atm, but DH & I have been pretty on & off over the past 2 years. Even when things are ok, he mostly works away, so I'm home alone alot.
TBH, I now crave the alone time. I love having the bed to myself, having DS in there... we co sleep full time when DH isn't here, & being able to have the older kids in bed with me if they are sick or something. Makes my life a bit easier.
My MIL got past the noise thing by sleeping with the TV on all night. Even now she has been married for 18 years she still can't sleep with the TV off. I got a dog, but only coz that was possible for me. Having her in the backyard & knowing she'll bark is enough to make me feel safe. I also sleep with the phone & my mobile beside my bed. I used to shut the back half of the house up too. The half with all our bedrooms. The smaller area made me feel safer.
Take your kids to the park & down for hot chips at the local cafe & just get out of the house. You might not get much adult conversation, but getting out of the house just for an hour or so every day helps you forget that you are lonely
After a while youll start meeting other mum's. It might be a while before you have a heap of people to hang out with all the time, but you will. I have a good friend I either see or talk to on the phone every day, then we have a bigger group of friends & we all go down to the club with all the kids (at least 10 all up!) for the weekly meat raffles. Or we'll meet for coffee or something. Avon parties etc. We all have kids & all have more than one, so we are all in the same boat. Not many of us get to go out partying, lol.
Just give yourself some time. Enjoy just being able to concentrate on you & your babies. You can put in so much more time with them when they are the only ones your thinking about. & when that crappy relationship is out of the way, you are happier with them & more patient, as well as having loads of time to keep the house clean! lol.
It will get easier