Find a plumber who offers a payment plan.

You can try a bigger snake. Rent one. It's worth a shot, since it's the exact tool a drain person would try first, and renting one for a few hours will cost less than a plumber coming out to do it.

If that doesn't work, you'll soon be spending more than what a plumber would charge buying stuff that you don't know how to use in order to maybe fix the problem.

A drain company will have several snakes, an inspection camera, a pressure-washer based drain clearing device, etc, and they can change techniques every time one of them fails. Going through the same process buying/renting stuff every step of the way will quickly get expensive.

One of the other problems with drain clearing is that there is some voodoo involved in reasoning about how the system is put together and where your snake is going. Plumbers have intuition about this based on the age of the building, materials used, construction details, etc, but you likely don't and it's not really easy to teach that knowledge. Sometimes the right way to get to a certain part of the system with a snake is not intuitive.

Good luck.

Homedepot (and elsewhere) rents out motorized snakes that are 75'+ long. Snake it from the roof vent down.

I’m a licensed plumber. If you can get ahold of the snake again undo the bolts and pull the toilet and try snaking through flange in the ground and before putting the toilet back you need to re install a new wax ring (very low cost) just so you don’t have leaks under the commode. If that doesn’t work try to find your cleanouts outside your house and snake through the one furthest from your house that one in most homes should be going inside the main under your house. All else fails that hole that was cut and never covered is going to be a major problem and roots will make way towards that feeding supply for them and also dirt and debris will catch on a hole in the pipe causing build up so that needs repair. At a hardware store they should sale what’s called a CT or rubber boot of the size of pipe that the hole is in and you have to just cut the section out and use two of those cts to re attach a new piece of pipe. If you have any questions contact me through pm if possible.

Have you called the city and explained the situation? Get on social media and comment there. Most city councils hate bad press. You could also go to a local media station and see if they're interested if the council refuse to help.

This is all if you're sure the issue is being caused by the work the council did.

I bought a 100 foot long pressure hose, a metal spray nozzle, hooked the hose to a borrowed pressure washer, and pushed the hose down the service line. When plumbers do this they can run a camera to verify the location of the clog before hand and then run the camera afterwards to verify they cleared it. But I refused to pay the $1000 the plumber wanted to charge me and just took my time working the line with spray nozzle back and forth for about 15 minutes. Line was successfully cleared. Total cost about $150

Can you get a hose into the cleanout? You could try a drain bladder. They are cheap and easy to operate. Attach the bladder to a NEW hose and slide it down into the cleanout and turn on the hose. The bladder will inflate and seal the pipe while putting water pressure against the clog. With luck the clog will blast out to the main and your pipes will flow again.

Easy and cheap. Has saved our house and my neighbors.

https://www.lowes.com/pd/Cobra-Rubber-Bladder/1000765778

Some video I found and didn't watch. Should explain how to operate. Super easy. https://youtu.be/G2Varyz1AWA?t=154

Pay attention to what you are doing and make sure you don't flood your house or something. Good luck! I believe in you! Don't blame a stranger on the internet if your problem gets worse.

Roto rooter is like $150 to snake out the line. More like $250 for weekend and after hours. Professional and they get it done right.

Do you have a waste cap or clean-out anywhere on the exterior walls? It would be a pipe with a cap somewhere outside perhaps.

If your on city sewer it sounds like you have a clog between your house and the city. You need a long auger snake to clear.

Try snaking from the toilet closest to the alley.

You call a sewer cleaning company, ask them what the rate is a for snake, and find the change to pay for it. Around me, it’s $100 for a snake, extra $50 for camera.

I used to have a main drain line that clogged every other month or so, and I would fix it by running a stiff garden house down the clean out before the clog with a metal firehose type nozzle on it. I would run it down until I hit the clog, then turn on the hose and push and pull it until the clog cleared.

However, your main drain line clogging constantly is an indicator of a larger problem - it is wider than your house drains so it’s likely there is a problem in the drain line that needs to be addressed. In my case, a tree root had entered the main line and it was about 75% blocked. I had to have that section of the line replaced. I tell you this because in the long run it might be necessary to have a professional diagnose the issue. See if a plumber would just come to run a camera through your drain and diagnose the problem. They might also apply that fee to the cost of a water jet or auger clean out if you decide to do it. I understand money might be tight but this may not be a DIY job.

City isn't fixing it? If they clogged it they should be liable to fix it

Call a legal help center. The city made your home unlivable for your children by damaging your plumbing. They should put you in a hotel until it’s fixed.

Find a way to afford a plumber. No shower for a week? It’s worth it

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You say you have one clean out near the house and one near the alley? Try hosing from the alley one towards the house to loosen blockage.

For now stop flushing anything other than human waste down the toilets. You most likely have a big belly somewhere full of fat. I would try to flush with your hose from the clean outs and snake from there too. Call the city and see if they can flush the main line or at least clean out your service line up to where they can to rule out it being their responsibility. Sometimes if you plead your case they will help you out and go up your service more than they should to help with the problem. Ultimately you need to have the line inspected with a camera to determine where the back up is. How old is the house?

There is a thing called a rubber bladder u can buy at home depot for cheap, it's really good at clearing clogs. You attach it to a hose put in into ur pipe, when u turn the hose on it swells to the size of ur pipe so water can't go backwards. The water is forced forward with increasing pressure and clears the clog.

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Look for a drain clearing company.

Do you have any matches and good insurance ?

try something like this?

https://www.amazon.com/dp/B0149L455G?ref=nb_sb_ss_w_as-reorder-t1_ypp_rep_k0_1_12&amp=&crid=1YBZ1RZ9CMVNY&amp=&sprefix=drain+opener

Find the money.