The Vogue is made by dutch people whom are know for flat surface and extensive ridding.
If that was my bike, I'd try changing the chainwheel first. Installing a smaller chainwheel has been suggested several times already, and by other members. For my particular bike, I tried 42T and 48T, before settling on 52T as best for both towing trailers uphill and speed over the flats. You probably should go slow when carrying kids around?
Then there's "start current". .....If you up that to 100% and keep current is 100% you'll fly like a rocket... and your battery will be cooked in no time at all.
And that's exactly what my bike did, during the brief time my motor was unrestricted. Sadly, I discovered it was illegal to have so much fun rocketing about. These days it zooms to 25km/h, at which point assistance rapidly diminishes.
Then there's "start current". That determines how much current is applied on the first turn of the pedal............................and on start, you're wrecking your chain/cassette pulling that weight.
My "Start current" was originally 20%, which made the bike jerky when pedal assitance started applying power - I can imagine this being useful offroad, to get the bike over tree logs , roche moutonnees and sleeping bears etc, but it made my small wheeled bike jump forwards, making U-turns and control difficult. Overall it was set up badly and I was on the verge of demanding a refund, but after changing "Start current" to 10%, and adjusting other parameters, my bike became a joy to ride.
(Both "start" and "keep" are relative to "levels" typically 1-5 or 1-9 being set suitably too as a % of total). You could in theory set-up say levels 1-5 for max assist hauling kids up steep inclines with no effort, and levels 6-9 for sensible assist for when you're not and not killing your bike.
I'd like "Start current" be completely independently assignable for each level, but it's not currently possible.
keep current is 100% you'll fly like a rocket... and your battery will be cooked in no time at all.
That's a very important consideration - I posted photos of the cells my 19.2Ah battery contains, and
@Nealh kindly determined my battery is capable of discharging about 25A maximum continuous current. The OP's battery is only 13Ah, and cell manufacturer and type isn't mentioned... vague on the Vogue website.
All of my heavy trailer hauling was done when my controller had been limited to 15A, and it has never failed to drag a trailer uphill. I thought it might with one particular load, but my quick release rear axle got yanked out by that very heavily loaded trailer on the flat, well before I'd dragged it to the hill.
If you like the natural feel of torque sensing motors, you need a throttle to climb hills effortlessly.
that does not solve the problem for his wife. Only a throttle can do that.
One way to solve this could be inned to add a Throttle controller.
Your wife needs a cadence sensor like the BBS02 or a TSDZ8 with a throttle, both are capable of 120NM, to winch herself plus the kids up a steep hill without relying on leg power.
The OP can add a throttle to his M400/80Nm or any of Bafangs M range, including the M600/120Nm... Cheapies start from about £12 on Ebay.
Not as eye-watering as being guillotined by some dude smoking Gauloises wearing a onion necklace, but aren't fines for illegal ebikes eye-wateringly expensive in France? The OP should bear this in mind, and research the relevant local laws before deciding whether to install a throttle.