Like mrsm43s said. If everything you normally pay out, over the year is included in bills, then it is very doable.
I have pots of money for everything so the £50 would be doable for me. That would be to cover incidentals like an afternoon out.
And contrary to what someone else said, of course you can go cinema for that. Meerkat movies and sat morn cinema are very cheap and you can buy treats at supermarket before you go. You could also eat at a beefeater type place within your budget as 2 adults and 1 child, your baby would not be paying anything. Even in 2 years time as baby grows, you can still have treats if you truly have included all bills and regular amounts over the year.
Buy a one day travel policy for around £2 every year on compare the market and gain access to Meerkat movies bogof at cinemas and Meerkat meals which is bogof at thousands of restaurants.
Most people should include these amounts anyway, as they know that Xmas, birthdays and school uniform are once a year. It's also always worth it to have an home fund for applicances and maintenance and a car fund for Mot, service and repairs.
It's also not miserable if you truly want the outcome. Ask yourself what is more important to you? To look after your children full time on one income or to go outside the home to work for more income but having to outsource childcare. Bottom line is being a sahm worth it to you? Is it worth it to your husband?
For me it was more than worth it. Being frugal can be fun if it want it to be.