Hi Anna,
Welcome to Yangon!
There are mums who get together with their young children. Have you found the YEC google group yet? If you google: Yangon Expat Connection, then you should be taken to a google group that you can join. Each Thursday, there is a gathering at the British Council, but I can't remember what time. My friend, Vicky, runs it. If you ring the British Council, they should be able to tell you the time. Also, you could email me at: beckyinburma /!\ I AM A STUPID SPAMMER /!\ dot com and I will put you in touch with her.
Soon, there will be a new website launched in Yangon which should have a calendar listing events. It will be easier to find out what's going on in town.
Welcome!