10 rods is quite a large plot to get under control and it all depends on how much time you are willing to put in and what methods you want to use.
Glyphosate will knock the weeds down and get you through inspections if it can bee seen that you are steadily working your way through the plot improving the soil and growing crops. If you don't want to use a herbicide then you will have to keep the weeds down by strimming and covering with black weed control fabric until you can dig the perennial weed roots out - it's a more expensive option than glyphosate and a hoe and much more time consuming.
As someone who inspects plots, I would have expected you to have had it under control by now. We usually give just encouragement and advice the first year and then expect a nearly well managed plot by the second year and definitely by the third year.
If your main problem is weeds then you really need to visit more frequently. If you run the hoe over your plot once a week at the height of the weed season you will have very little problem and the job will be easy.
We have 10 rods (but no small children now - we did have when we started allotment growing). I would say that we average about 5-7 hours per week each (2 of us) during the growing season and about 2-3 each during the cooler months.
If you don't have enough time to keep the weeds under control than you'll have to do a lot of mulching and use weed suppressant fabric. Don't let weeds produce seeds as this will annoy neighbours and make your job much harder to control fresh growth in subsequent years.
There will be lots more people around to give you advice so you can pick and choose which you take
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