I think you need to take a step back and look at your current situation and commitments and where you want to be, and then work out a solution to get there. At the moment you've found a solution but it may not get you to where you want to be anyway (timescales, availability, proximinity to family or good schools).
Completely aside from the waiting lists for the council housing, and the possibility you won't qualify due to your husband's visa status, waiting on an offer of a council house leaves your future entirely out of your own control. If and when you get offered a property it may not be near a good school (unfortunately schools in areas with high levels of social housing often seem to be performing more poorly than those in more affluent areas), or they might offer a property not near enough to your parents. It may also not have other features you'd consider desirable (parking, well insulated, access to a garden, up many flights of stairs, have noisy neighbours etc).
There is nothing to stop you joining the waiting list (assuming eligibility) and seeing what happens. However in the meantime I'd try to find a time when the little one is asleep to sit down together and make a plan. Where do you want to be realistically in 2 or 5 or however many years time. So for example if your priority is being able to rent a 2 bed property of your own that's an achieveable goal, what kind of monthly income after tax and self employed expenses for your DH do you need to have to make that a reality in the area you'd prefer to be in? If your priority in life is near a good school, parents, and having enough space then it's likely something else will have to give and usually that's time. You don't get to be a SAHM might be a compromise for example, you go back to work after maternity leave and your DH shifts his hours to work 3 week days and the weekend, and takes care of the kids the two week days you're teaching, they have 3 days in nursery under the free/cheaper hours and you look after them at the weekend. This is not a forever plan, it's a few years plan. You might decide actually the area is something you're willing to give up, and live near a worse school, or further from family so that your rent is cheaper. You might decide that your goal is actually bigger and you're prepared to sacrifice more now to make it happen, you want to be in control of your property and you want to buy, so for a few years you're both going to work extra hours, a second job, whatever it takes to buy your property and have cheaper living costs and more security that way instead.
I am a firm believer that sometimes we're just too close to the problem to see all the possible solutions, and sometimes we need to step back and evaluate all the options (even if some of them are an absolute no for you, they are still an option to be considered and it can help mentally to know you've looked at everything).