Update: Thank you everyone who responded so thoughtfully. We decided to shorten our stay to afford a nice Ryokan, with a private bath, and meals. I think we will enjoy ourselves more, and then go adventure somewhere else after Hakone.

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Our family of 4 (including a teen and tween) will be in Japan for 15 days in November (mostly Tokyo), and my husband wants to get away from the hubbub for a few days in the middle to relax. We had honed in on Hakone just for easy access from Tokyo, and he likes the onsen, pirate ship, and ropeway. We originally booked a Ryokan with Onsen, but with my sizable tattoo I wouldn't be able to use the facilities, so we re-booked at a small rental house, but it doesn't have a hot spring access. We've looked for a place with a private onsen, but whoa, $$$. I'm wondering:

1. Is 3 nights too long in Hakone? Is it better to just splurge for a nicer place for 1 night? Is 1 night even worth the hassle, time or transportation etc?
2. Is it better to just get a cheaper place (non-Ryokan) and then try a day onsen like Yuryo? I'm hearing mixed things about the tattoos, that it's ok in private onsen, but their website clearly says no tattoos.
3. Will having "just a place" that isn't a Ryokan or spa hotel defeat the purpose of being in Hakone?
4. Is Hakone too sedate/boring for kids? It seems like after the Open-Air museum, the boat and the ropeway there isn't much for them except hiking? They're good sports about exploring, and they are foodies, but they don't really have interest in onsen.
5. Is there a better alternative away from Tokyo for a relax? Nikko? Kawagoe? Kamakura?

Thank you!