Hun, it's my understanding that unless you leave the hospital walking they will not let you out unless you have a carseat and know how to use it. Even to leave in a taxi I believe they make you have a carseat.
There can be waiting times for new ones, one girl on here waited 8 or 10 weeks for her carseat to come into the shop, so really you should have had this organised a while back. But you are where you are, and you have to look at your options. You can't afford to buy one, you don't need one particularly often and as far as I can see this car seat is reasonably new (seems to be about 3 years old so its not like 10 years old and out of saftey standards, but I am sure you can look this up) and I presume it's not been in any accidents? It's your MIL not some stranger from ebay so you should be able to know if she would lie about it having been in an accident. So all in all, I don't think you are in a great position to refuse just because its not the pattern you want.
Ultimately its your baby not your MIL'S, so it's your choice thats for sure, but it's also your responsibility not hers just because they have more money than you. Your baby hun.