Definitely no point changing the car, you'd be worse off safety wise.
There is no safety difference between belt fitted and isofix fitted as long as the belt fitted seat is fitted correctly, which means correctly tensioning the seatbelt and making sure it's tight - most people don't realise to do this, which is why seatbelt is considered "less safe" - it's less safe if it's not done correctly.
The safest and longest lasting rear facing seats aren't isofix. Have a look at the Britax Max Way, which is on offer at the moment, really compact to fit and easy to use. It does have a leg but it doesn't sit as far forward as an infant carrier. Because they are for older children, they sit much more upright which is how they take up less space. It will last until 25kg which is a good couple of years longer than the seat you're using now if it's isofix, so DD2 could go into DD1's current seat when she outgrows the baby seat and DD1 wouldn't need to vacate hers.
You may also look at a less bulky isofix rear facing seat - we found our Joie 360 Spin takes up less space than our infant carrier on the base, again because it's upright and spaced quite close to the back of the rear seat. Or, expensive (but less money than changing the car) what about Axkid One - it can contract down to be absolutely ultra-compact, fits using isofix and is rear facing up to 23kg. Which? Best Buy both for ease of fitting and safety.
The tightness of the belt is particularly an issue for forward facing, so if you're looking at forward facing seats I'd look for either one which is isofix (especially with top tether, if you have the top tether anchors) - avoiding the spin/multi direction feature tends to mean that the seat sits further back in the car. Or if looking at belt fitted, a seat with belt tensioners is a very good choice. If the seat doesn't have tensioners, you want to kneel into the seat when pulling the seatbelt tight to get it as tight as possible.
I'd look at these options:
Britax Advansafix (best rated seat that converts to booster)
Joie Bold (if you need harness over 18kg)
Maxi Cosi Beryl (even better option for harness over 18kg, but more expensive)
Britax Trifix 2 (best rated FF seat with 5 point harness)
Cybex Anoris T (best rated FF seat overall - high price tag, experimental solution)
Maxi Cosi Tobifix (best rated FF seat without top tether)
Seatbelt fitted
Maxi Cosi Tobi (good belt routing over and under, tensioners, best rated FF seatbelt fit)
Britax King (built in tensioners, easy to fit)
Britax Evolva (best rated belt fitted seat that converts to booster)
Another solution might be to fit the baby seat without the base. That's just as safe (actually a lot of seats score slightly better without base) and easy to do and doesn't have the tension issues.