If those are dumb switches it is going to be near impossible to troubleshoot. You likely need at least interface counters to isolate the problem.
How easy is it to reproduce the problem? or how random is it?
If you can recreate the problem in 60 seconds, you could simply try unplugging the shed and verifying if the house stops dropping. If it resolves, plug in the shed and unplug the granny flat, etc. Ultimately, some way or another you will need to isolate it.
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If it was my own money, I would just rebuild this mess, but a customer probably wants it fixed labor only and for $100. Have fun with that.
My recommendation personally would be to get a tiny Palo Alto or Fortinet firewall otherwise if the budget is tight do Packet Fence on an ARM device to the Internet. From there, I would connect a PoE++ switch probably a 12 port Cisco or if the budget is tight in order: Meraki, Ruckus ICX, Aruba, Ubiquiti switch instead.
Since the only reason for the Switch is run Access-Points, I would NOT have any other switches in the topology... Instead the {rear, front, shed, granny_shack} would all get an Access Point. If needed, I would pull new copper CAT6 otherwise if I was lazy, I would attach an RJ-45 plug and then a keystone jack and join the cables. Regardless, I would wire it all as a star topology, so the ideal fix would be to pull a network cable from the granny-shack back to the front and not have any connections anywhere in the network cable.
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Now, if they really want switches in all those places, I would make sure they are all PoE++ switches of the same brand in the order of preference above. Regardless, I would ensure there is a minimum of SFP+ supported on each switch and buy some cheap probably $11 transceivers on FiberStore... Presumably the 10G BASE-SR, so I could use cheap multi-mode fiber. From there, I would just buy OM3 or OM4 50/125 (aqua or perhaps purple) fiber with the LC to LC connectors already installed in the proper lengths. It would be maybe $5 per meter for the fiber, so very cheap.
The reasoning is with all the computers and wireless, if any device misbehaves it can consume up to 1 Gbps. If you have 10Gbps among the switches, even a layer-2 shitstorm probably will not significantly adversely impact the network resulting in drops or latency provided you buy decent equipment with good ASICs.
Most of the networks I build today use two 100G-BASE-FR single-mode QSFP28 form-factor transceivers on each end for LACP. I generally do 200 Gbps between switch stacks, but I have not had to do granny sheds.
