OP does seem to have a bit of an apples, pears and bananas problem.
Apparently the apples are her 2.5 day salaried day job in band M6, with an FTE salary of £43,607. Apparently teachers are paid for doing 195 days a year, so this is a gross day rate of £223.63. In a permanent M6 role, there is all the PPA, training interation, report writing & parents evenings etc, so it's certainly not limited to 6.5 hours a day. Lots of teachers say they work a 50 hour week in term time, so let's assume 10 hours a day is the realistic workload to get an M6 permanent school role done for the 195 days they are working. This means the gross M6 rate would be £22.36 an hour, or thereabouts.
The pears are the supply role at £140/day for 8.30-3.30. I expect the agency considers this 6 hours paid work, but if I generously allow only half an hour unpaid for lunch (which would decrease the equivalent hourly paid rate rather than increase it). £140 for 6.5 hours supply work is £21.54 an hour gross. Turn up at 8.30, leave at 3.30, no parents evenings or reports.
Seems like it's really not that far out of the ball park from the permanent role on a like-for-like basis.
OP then threw some bananas in the mix, saying that cleaning work is available locally at £16/hour. This is the gross rate obviously. Out of this you would have to pay £3.45/week Class 2 NICs for your self-employed work, plus 20% of everything in income tax (as it's a 2nd job, just like the supply work) and usually for that rate, purchase your own materials too. If you worked 6.5 hours a week as a top-up to your main job (the same as your supply day), your take home would be £79.75 before the purchase of any actual cleaning materials. No looking so flash compared to the £112 you're grumbling about now, is it?
So for comparison on a like-for-like gross basis, the roles seem to be:
£22.36/hour M6 permanent (but this is annualised & paid in 12 equal chunks)
£21.54/hour supply with current agency
£16/hour cleaning work - own Class 2 NICs to pay, materials to buy & tax return to complete.
£11.44/ hour national minimum wage - lots of retail, much agency cleaning work, plenty of entry level receptionists etc etc
Entirely up to you OP how you choose to spend your time, but do assess on a like-for-like basis rather than grumbling about fruit salad!
You asked for opinions on whether your DH was fair in thinking this is a decent wage.
My opinion (particularly as you didn't read a contract before agreeing to the agency work - who does that? 😳) is that the hourly rate you are currently paid for no-commitment supply work is decent yes.
Don't think the streets will be paved with gold if you swap to cleaning, that's for sure!