Do you have isofix in the front? I assume not.
If your current seat doesn't feel very secure you might have what's called forward anchorage - it's common in front seats with this seat because the belt path is quite narrow. Try pushing the child seat into the vehicle seat cushion, and pulling the seatbelt through to remove any slack and then re-fix the belt clip.
If the seat still feels wobbly and unsafe, loosen the seatbelt and move the front seat slightly forward, then try fitting the child seat again. Repeat until you can get a solid fit. A belt fitted seat should still feel secure, not wobbly.
It might also be best to fit it in the back for now since she's so little and the airbag can be a danger to children when they are forward facing. It might be easier to get a more secure fit in the back.
I agree that Britax Max Safe Pro might be worth looking at, it's reduced in a lot of places to £179 because the Max Safe Pro 2 has just come out. Because it's belt fitted, you can have it in the front or the back (you need to disable the airbag if fitted in the front, and ensure visibility of the side mirror) or Axkid Minikid 2, which is about £224. Those seats will let you rear face up to about 5-6 years old which will easily be enough time, and they don't take up a lot of space in the back.
If you're worried about committing to RF in case the travel sickness gets worse, I would probably prioritise a brand which has a good track record for FF - so probably Britax Dualfix M Plus or Pro 360 depending on what colour you prefer for the better offers. This is isofix only and would need to go in the back, but it allows RF up to 105cm/19-20kg (depending on model) which might be sufficient if your DD drops down from her current centile, which some children do.
Or Maxi Cosi Mica Eco is about £170 at the moment in a lot of shops. Again good record for FF, still want to stay RF as long as possible but you have the option if you need it.
For a cheaper front seat option, Graco Extend R129 is under £100 at the moment, this is RF and FF and belt fitted. It doesn't last as long as some of the other 105cm seats - but if you do end up changing to FF later on, you could then potentially replace it with something which has a top tether perhaps, as there are some 125cm FF seats on the market now.