Hi Jenny... I can sympathise with you on the weather - I live in the West of Scotland so I've experienced the odd bit of rain
Interestingly, flower shots can look wonderful just after the rain - I know
@susiejb takes some magnificent macro shots with water droplets hanging off petals etc. It might not be what you're after but it's worth looking at some of her images in those sorts of conditions! (Sorry for the call out, Susie but you know I love your macro flower shots...)
Indoor lighting is all about getting the quality and amount of light right. That's "all" there is to it... however, just those two things (especially the first) are actually massive areas with so many variables. For the size of subject you're shooting, natural window light is lovely because the window is many times larger than the subject, so you're basically getting a big softbox, especially since you're shooting on overcast days with diffuse light coming in through the window.
The downside is that because it's sunlight, you can't easily control it's power or direction, but of course you can cover the window with muslin if you need as well as move the subject closer and further away from the window and change the relative positions between camera, subject and window. You're introducing a reflector which adds some fill light into your images so that's another variable to consider. You can change the power of your fill by changing the size of the reflector and/or its position. Moving it further away from the subject (and further from the window) will reduce the power of the fill as well as make the area filled in with light smaller. Obviously reducing the physical size of the reflector reduces the area filled (as well as slightly reduces the power).
The other "issue" of course is I bet your room has white ceiling, light walls - basically making it one big light tent
So you're getting some amount of fill light bouncing around no matter what you do with your reflector...
Looking at your images, the ratio of main (key) light from the window to the amount of fill light from the reflector is a bit too even. I would start by taking away the reflector completely and looking at the image just windowlight produces. This is the least amount of fill you can achieve unless you start hanging up black drapes around the room! Do the shadows look a bit too deep? If so, you may well need to add some fill with your reflector card. Alternatively, aren't there enough shadows? If that's the case then your "room fill" is contributing too much light... so take a large black card (rather than white reflector) and hold it by the far side of the image - this will prevent as much room fill hitting the opposite side of the image and should create deeper shadows. Take a look at the image (either with your eyes or taking a photo) and compare.
The other benefit of sunlight is you can see you changes "in real life" so you don't necessarily have to take lots of photos - look with your own eyes at how movements to black cards/reflectors change the light that's falling on your subject.
Sorry, that's a bit of a whistlestop tour and apologies if I'm explaining stuff you already know. Putting black cards around your subject on the non-window side, back and potentially even front (with a gap or hole to shoot through) will help reduce the amount of fill if you are shooting in a white room. Once you've got the amount of room fill reduced to a level which is ok, you may find you need to add some specific fill - or not. Have a play!