L.P.
We had a very lightweight, compact stroller that had all the bells and whistles of a larger stroller. It was a BabyTrend Passport. It is not an umbrella stroller, so if you specifically need a stroller that folds up like an umbrella, then this won't work. But if you don't need it to fold up like an umbrella stroller, but just need a lightweight stroller that folds compactly, this one is really nice and might work for both of your scenarios. It has a parent tray with cup holders, a child tray that comes completely off, so no scratching when you fold the stroller, and it has a reasonably big basket for a lightweight stroller that you can actually get to. I've never seen a bigger basket on a lightweight. I used this stroller with my son way after he had exceeded the weight limit, and it still functioned well. We bought ours at Toys-r-Us, but on their website, they say it can be purchased at Baby Depot (Burlington.) It's pretty inexpensive, too, which is a plus, but excellent quality for the price.
http://www.babytrend.com/strollers_single/1511.html