Time, yes you can. And in my experience, LEAs are either neutral or helpful. Mostly neutral- not a good idea to expect actual help and support- you need to find that in other places, but you will be very unlucky indeed if they are actively unhelpful.
There are loads of free and virtually free resources- and there are libraries, and charity shops full of books!
Can I suggest that your first step is to find out about HE groups in your area? And things like sports and other clubs for the appropriate age groups. Is there an active and good (they vary a lot) beaver/cub/scout troop? (One of the cheapest ways to provide outside the home activities and sociability) Do your research. Unless your children are a crisis point in school, take your time and plan.
Think about why your children are unhappy at school- is there anything you can do about it? Is it the particular schools? Or are they just not "school shaped"?
Think about the bits they do like (if any) and how can you make sure they still get those bits. Sometimes this is where money rears its ugly head- my ds for example, plays in every team going at school - even if I could find the same for him in a HE environment it would cost an absolute fortune in club subscriptions and petrol. Ditto my dd with music and drama, and her social life!
If any of your children have any additional needs, think about the cost of assessments and statements and additional resources. These are often incredibly hard to access thought the LEA but they are there- if you are HE there is a lot you would have to pay for yourself.
Think about yourself. Is this something you will be happy to do for the foreseeable future? How would you feel about very little time for yourself, particularly with small children. Who would support you? What if your circumstances changed and you had to go to work?
And once you have done all this and you have decided it's something you can do and want to do, talk to the children. Remembering that you can always give it a try, and go back to school if it doesn't work for them. (Oh, another thing to research- would you get school places later if you did decide to go back?)
It's a fantastic, wonderful and eye opening thing to HE. But it's not easy!