OP - don't look for excuses to not go out/make things happen - or you'll become a self-fulfilling prophecy and, nothing will happen.
You can join meetup.com to make friends to socialise with for days/nights out, you can pursue hobby, etc. Internet dating isn't the only option, you could come across a nice man whilst doing something you enjoy. There are also friendship sites, there's Gumtree, newspaper ads etc loads of women seeking friends for occasional socialising. It happens - women get to the stage where friends are married and socialise less, or move away.
You can pay for sitters - unless you plan to be out 24/7,its not going to be expensive. Use an agency, or some mums at school will be sitters.
I'm presuming you are in the UK? If so there are numerous daytime activities, adult education classes, all sorts. Things don't only come alive at night!
Again as said, hard as it can be to get 'out there' - if you dont decide to do something from the numerous options out there then you're far less likely to meet anybody. We don't live in a country where its hard for women to get out. & you're not housebound, are you? So - go out. No matter what, you're the one who has to make life happen for you anyway.