In answer to your question
No you shouldn't get a kitten. Your family member shouldn't be
selling them to anyone, kittens shouldn't be a sideline to income and should only imho be sold by registered breeders or rescues. They should have got their cat netuered and then they wouldn't be offering them out to relatives who hadn't been considering getting a cat for free.
You want a kitten to see it grow. Well they don't grow for very long and then they are adults, then what? It sounds like you have already had cats that your parents now have and as you couldn't offer them forever homes perhaps taking on another isn't a good idea. When you got those cats it was a commitment, you couldn't honour that commitment so you shouldn't be even thinking of getting another, just cos a free one is available.
Just because you CAN get PDSA doesn't mean you should take advantage of it. Have a look at their website they are looking for funding from donations, wills and a shop to raise funds for cats and owners that need it. Why taking their funds? Perhaps the PDA's funds would be better applied for people whose circumstances changed
after they got their animal. Like redundancy or ill health. Perhaps if your circumstances are changing and you won't need the PDSA you should wait till then. I'd love a Ferrari but I can't afford one.
Having an indoor cat can work but I would suggest you get an indoor CAT than needs a home rather than a kitten. especially when you have a baby. A young kitten and a baby are demanding. plus in the future your housing circumstances might change. This landlord might be happy for you to have a cat, your next may not and you need to think past the kitten stage.
The fact your cousin is struggling to find home for the kittens should tell you that rehoming is a problem and the fact you never wanted a kitten or cat till then makes me think that you shouldn't be getting one. I planned and wanted a cat for ages before getting Ella and Effie, it was a conscious and informed decision and not because I knew someone that had a kitten. At first my decision was to have them as indoor cats, although that changed so I don;t have a problem with indoor cats but everything in your post other than that makes me say no..
Sorry you asked for an opinion and my personal opinion is this isn't the right time for you to get a kitten and this is a living, breathing animal you are talking about. I know this will come across rude and I am sorry but your slant on getting this cat comes across being quite naive and actually selfish and there is too much wrong with what you are saying for me to smile happily and say "oooh yes get the cute little kitty"