What about a schulter edge? See a post below to see what I mean- think that will solve your issue in a lovely way.

Here is pic of the dreaded low window with new cabinets installed. As I mentioned we are going to be installing Verde Peacock granite. Have no clue what to do for a backsplash???

CKGM I don't see the post on the schulter edge. I have no idea what it is but would be thrilled if it can work for me and solve this problem. I am going to google it now. If you can, please repost what you wanted me to see. Thanks a million for responding with some advice:) You guys on GW are the best. i feel like an amateur who has so many great personal consultants that i can count on for help! :)

How about having your granite go up to the bottom of the window sill for just the width of the window? You could do your tile backsplash everywhere else you want it. I think it would look strangle to try to fit you backsplash tile in that 1inch space.
I think some one posted recently about continuing their granite up under just the window sill and the width of the window. Maybe someone can search for that post

What if you used a strip of mosaic tile underneath the window? The tile comes on a mesh back, and cutting one row would be very easy.

Two suggestions.

1. My trim carpenter told me, while trimming my three kitchen windows after doing most of the rest of the house in the reno, that most kitchen windows are just trimmed on the top and sides. They don't have the bottom trim piece to leave space to accommodate the tile. Could you re-trim the window to take off the bottom horizontal apron? I think you'd just need to have the two side pieces cut straight across from the shortest point of their current angle cut. Then you'd have enough space for tile.

2. Run your granite up that small 1" of wall space just under the window with tile everywhere else. BUT, I'm also not sure granite could be cut that small. When my fabricator messed up my peninsula marble so the gap between it and the wall was too large for me to go without a bs like I had planned, we talked about fabricating a narrow strip of marble to hide the gap. They suggested 4" tall strip. I strongly objected. I ended up with a 2" tall strip, which I *think* was as short as they could go. You might ask your fabricator.

Good luck! You've got a lot going on, but will enjoy your kitchen when it's done. Won't be long now. :)

Here is the post badgergal mentioned about the granite backsplash going up to below the window, and only below the window. I posted it but my problem is a little different, as I actually don't want a backsplash anywhere else on that wall, and I think it sounds like you do. The link has some pictures that may help you.
However, I think your solution is, as breezygirl mentioned, to remove the bottom trim of the window. Here are some photos from Houzz, as you can see when there is no under the sill trim you get a nice clean line.

[Traditional Kitchen design[(https://www.houzz.com/photos/traditional-kitchen-ideas-phbr1-bp~t_709~s_2107) by San Francisco Interior Designer Brownhouse Design, Los Altos, CA

[Traditional Kitchen design[(https://www.houzz.com/photos/traditional-kitchen-ideas-phbr1-bp~t_709~s_2107) by New York Architect Crisp Architects

Here is a link that might be useful: Backsplash just under window

If they can't do the granite it would be easy to put tile there. As said above you can do a strip of mosaics or use liners (long narrow tiles). We had a issue in our bathroom where the tub meets the floor. Put in a strip of 5/8" mosaic tiles and it looks great. People think it was planned that way.

I don't think it's a problem at all. We actually put in 4 new windows and intentionally used the tallest ones we could fit - there's probably 3" between the window and the counter, not 1" but if the standard window size had left 1" above the counter I still would have done it to get the maximum light and view.

I second what breezygirl said about the casing. If you take the bottom piece of casing off and replace it with a stool, it'll give you at least another inch, possibly a smidge more. Then you can run whatever you use for the rest of your back splash underneath. Here's a photo that shows in more clearly:

Duh! I should have posted the link to what I was talking about. Here you go...

Here is a link that might be useful: Schulter edge

I would have the trim carpenter re-trim the window....get rid of the bottom piece of trim and the mitered corners and have him add a sill that is wider than the side trim. Then have him add an apron that meets the counter. If it's made out of azek it won't rot or be damaged by the water.

Then just have the tiler run the tile up to the edge of the apron and you're done.

Just trim the tile to fit. It's not difficult. I don't know why the tile store people told you that, unless they didn't want to deal with cutting. We had the same situation with our kitchen window. Only 1" of space under the window. My husband did the backsplash himself and did a beautiful job. So, you don't have to be a professional to do a good job. It is a much better solution and probably much less expensive than changing out the window trim. It also looks as it was intended, a continuous run of tile and not as an afterthought as adding counter backsplash in just that area might.

In our last house we had about 2 inches between counter and windows. I had the granite fabricator cut a strip of our granite and bevel the two ends.

Hers a picture of the bottom of my widest kitchen window to show you what I meant about the trim. Annie's diagram is most helpful.

Thanks everyone for all the great ideas. My granite guy and general contractor were great today!!! Both of them are so nice and worked together very well. The granite guy is the owner of the granite store and he comes out to do all the measurements. I am very lucky because I have heard horror stories about contractors being difficult! We decided to take the whole window frame off so that we can have a 4 inch backsplash. The fabricator is going to also create a granite sill so there will be a little shelf just below the window. I think he said the sill will round out about 1 1/4 inch on each side to give it a nice finished look. He really seems like he knew what he was talking about. At first my contractor said he would just cut off the bottom section of the window frame, but the granite guy said that he would prefer to have it all off to avoid any space issues when installing. My contractor said, no problem. He took the side pieces and bottom pieces off and will retrim it after the granite is installed! Granite will be installed Thursday morning at 8:00 am-- so excited tosee how it looks!!! :)
Now I'm thinking of painting the trim to match the color of the new cabinets. The trim is really a stock builders white color. Looks OK next to the Coconut color cabinets (which are an off white). I went to the paint store today and they matched up the cabinet color almost exactly- Benjamin Moore Cream Cloak. There is the window trim and then door trim that leads from kitchen, near refrigerator wall. The door trim is between cabinets near stove and pantry cabinet. What do people think. Leave the stock white paint as contrast or paint trim to match the cabinets???
The kitchen got a first coat of BM Capilano Bridge today- 2nd coat will be tomorrow. I think it is going to look good once the granite is laid- should pull out the caramel coloring within the granite.

So glad we were able to help.

You're putting in a 4" granite backsplash? All over or just under your window? If everywhere in the kitchen, then you must have decided not to do tile at all, right?

This issue is debated every now and then around here, and many think a 4" granite splash is dated. I could understand doing it just under the window....maybe. If you now have so much more room with the window trim off, why don't you just continue the tile from the rest of the room for a cohesive look?

Breezygirl- The backsplash will go all around the counter. I know there is an ongoing debate about the granite BS maybe being outdated. I could be making a mistake, but went with what my gut was telling me to do. If I really don't like the look of the granite BS then I believe can have it removed at some point down the road. I'm being optimistic and really hoping I like it. May add tile above at some point, but not right now. I will post pics after it is installed on Thursday.