Her blue dress with large sleeves

Can one say

a. They were driving around in their car with a new engine.
Meaning: They were driving around in their car which has a new engine.
or They were driving around in their car, which has a new engine.

b. She was wearing her blue dress dress with large sleeves.
Meaning: She was wearing her blue dress dress which has large sleeves.
or : She was wearing her blue dress dress, which has large sleeves.

c. They lived in their big house with a blue gate.
Meaning: They lived in their big house, which has a blue gate.
or : They lived in their big house, which has a blue gate.
?

I think (a) can be used both if they have one car and if they have more (only one of them having a new engine).
I think (b) can be used both if she has one blue dress or more (only one of them having large sleeves).
I think (c) can be used both if they have one big house or more (only one them having a blue gate)

I also think 'a new engine', 'large sleeves' and 'a blue gate' can be replaced respectively with 'the new engine', 'the large sleeves' and 'the blue gate'.

Is this analysis correct?

Many thanks.