I think that's a real good option.
A backhoe will be slow for doing any volume of work, but it's excellent if you want one around for doing a job once in a while without all the hassle of going to rent a mini-ex.
A mini-ex will allow you to do most of what you want in a weekend, and still time to do things you didn't know needed doing.
I borrowed Dad's mini-ex for 9 months (he got a newer one and hadn't sold the old one yet). It was excellent, but I learned why I saw him with a shovel out often. They absolutely destroy your lawn if you drive over it with any frequency. So many of the things I thought I might use it for I went and got a shovel instead. A backhoe wouldn't have that issue - so for me in a lot of ways I'd use a backhoe more than a mini-ex. And one fewer machines to store too.
