Please take this in a kindly way — I'm not sure how to say it otherwise.
There are literally thousands of programs which can edit JPEG files. Adobe Photoshop is the big name, but you can also use Gimp (which is free and open source software) or online editors like https://pixlr.com/. Even programs like Adobe Lightroom or Darktable which process RAW files can usually work on JPEGs as well.
Having RAW files would make the job somewhat easier, but isn't essential (see Good examples of RAW's advantages over JPEG?) — but as you note, the photographer doesn't have to give these to you (see If I paid for photography am I entitled to raw images? for more on this whole issue).
But, here's the thing... if you don't have the computer savvy to figure this out, doing a complex task like making a muddy river in the background look nice isn't going to be easy either. No software will have a "detect and fix river" button, and any alternation will involve painstaking work with the edges where the river meets the foliage or is behind the lace of the dress.
I think the photographer's estimate of an hour and a half per image to do a good job is completely reasonable. It might be possible for an expert to do something more quickly, but if you want the detail right and for the change to look realistic, there's no magic; it just takes skilled, artistic work.
How much is your time worth? How much patience do you have, and how important is it to get right?
Personally, I think I would just accept that the photographer documented the day as it was, and not look for a doctored reality. But if you — or, really, I think more importantly here, your daughter! — aren't happy with that, I'd consider paying what the photographer asks. As I said, not only is the time estimate reasonable, the price is quite fair. (I don't contract to do this kind of thing, but if I did, I'd probably charge twice that.) Pick your favorite five photos (or two, or ten — what's it worth to you?) and spend the money and be happy.
Or (as suggested by osullic), you might ask the photographer for black and white versions. This can look nice and artistic, and that conversion may be something more like 10 minutes per image. Assuming the same rate, perhaps that will fit better in what you can budget for.
As a footnote: although they are of your daughter's wedding, and although you have purchased digital copies, unless you have a contract which says otherwise (and this is rare and expensive), the photographer owns the copyright to the images. Among other things, this means that the right to make modifications rests with her. Although it's somewhat unlikely, if you make the modification yourself or pay someone else to, you could be liable for copyright violation.
As in If I paid for photography am I entitled to raw images?, this isn't fun to realize after the fact, but when paying for an artistic service like this, if you have special demands, you need to make sure it's all agreed upon and spelled out in writing in advance. The photographer is trying to make a living in a low-margin and cutthroat business; she can't just do out-of-the-ordinary work with no consideration and still feed her family. Of course, you have no obligation to provide her with a sustainable livelyhood — but you do have the obligation to hold up your side of the agreement.
