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I have a 9 year old and a nearly 5 year old on the back of mine. The 5 yo messes about a fair bit, leaning out to the side and rocking about and you can definitely feel it, a bit like a gust of wind but is easy enough to react to and counteract. Don't think your wife will notice it much while they are the size they are but might be an issue in the future if she isn't particularly confident. Haven't ridden an UA so no idea about a comparison.
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Long john's defo you are affected less by kids moving around.
Long tails if they swing around, the bike is going to change trajectory, but to be honest once you've got a few dozen miles clocked on it, the pilots confidence will go up and it'll likely be fine*. Kiddo's also learn to not swing around like monkeys after a few rides and a few telling off.
*Recently a customer got a stonking deal on a mk1 with pretty much all the options, as one of the owners/had a bad scare on the road when the stem /bar combo twisted around (was never done up from new, bought online, no one had checked it, owner had self assembled etc, the usual) and they crashed on a busy road with kiddo's on board, thankfully car's all avoided them. So they sold it for not a lot and a local family swooped in and picked it up and are very happy with it.
If your partner was taller I would say get a benno boost instead, slightly bigger rear area and other reasons (go back through mine and others older posts). But for someone thats under 5'3 or 5'4 the GSD is pretty much the only long tail that genuinely fits them. WE have a 4'10 and a 4'11 user of the mk1 gsd at our shop and they get on OK with it. I think R+M also make a long tail now that has a pretty decent stem/bar combo for shorter folk, could be wrong.
Anyone carrying two kids on the back of a GSD? My other half had a go on one yesterday and liked it a lot but is a bit worried about having the kids on the back if they start rocking around and misbehaving. They are 9 months and 3 years old atm. She's 5'2 and quite light so thinks it might be easier to manage them with an urban arrow or similar.