I don't know if it's possible to alter fat:muscle ratio of specific body parts through anything apart from surgery.
You can increase the muscle in your legs through exercise and decrease the fat throughout your body through diet/exercise, but I guess you knew that.
10 mins jogging a day, though infinitely better than nothing, isn't very much. Could you increase that to 12 this week and 15 next? Your body acclimates to what you demand of it so any (healthy) weight loss/muscle gain will plateau eventually - it's good to mix things up every now and then.
Weight training is brilliant in a number of ways - Henry Rollins wrote an article about it that's worth a read - but take claims that you won't put size on with a pinch of salt. I don't think anyone looking at me would notice, and I'm certainly not especially muscular, but a few weeks after I started lifting I found I'd gone up a size and had to buy bigger work shirts. I also grew out of a much-loved necklace.
Totally worth it though. When you lift weights, the numbers don't lie. You can't kid yourself that you've done well if you haven't. But when you do see that you can now press double what you could when you started, that's a good feeling 
To add to one of YouSay's points, treat any fitness product marketed exclusively at women with scepticism. Triple scepticism if it's pink. I was looking for recovery shakes not so long ago and came across that was especially for women and had "fewer calories".... Turned out it was exactly the same as that brand's men's product, they just recommended smaller servings 
Berni NHS state that safe weight loss is 1 - 2 lb a week, and you seem to be going at double that. Hope all is well.
Finally... If you ever watch sport in slow motion on TV, you will see that even the thighs of professional athletes wobble. To wobble is human.