@rich28uk
First of all: Congratulations on new baby. I don't know if the baby is your first or if you already have other kids. I've been a single parent for like 16 years, but my kids are now older and have moved out.
Wishing your new baby many years of well being health, but you have to accept that like with every parents and their babies, you would be expected to have to take your baby to see the doctor or to the hospital, and it could happen at a short notice.
So you can't afford to have your Discovery let you down just when you really need it, specially including tyre wear. It would be best if you can try to keep your car in good order, at the minimum basic needed by law, including tyre wear.
The problem with cheap budget tyres is that they would hardly last longer, you would end up having to spend on new ones every couple of years (depending on the mileage you drive). The problem with premium tyres is that they're expensive to buy to start with, and you need your money for the baby. Let alone worrying about winter tyres.
But in my experience when I had the Ford Focus, I did start off with budget tyres because they're cheaper, but found out that they hardly lasted long. Sometimes just a year, sometimes a couple of years. When the time comes for me to have to buy new tyres, I couldn't afford new ones, because sometimes it may be late August and I need the money on school uniforms and new shoes for the kids. It would be £260 (assuming £65 x 4) then a couple of years later, it would be another £260, and so on.
Few years later, I decided to go for premium tyres, it could be £400 (assuming £100 x 4) and they did lasted me much longer, like as much as four years (assuming if I cut down travelling a lot).
But if you think about it: Spending £260 for budget tyres, then two years later, you have to spend another £260, it would mean something like £520 in four years, compared to having to spend £400 on premium tyres for the next four years.
And bear in mind, some of the premium summer tyres could cope better-than-nothing in winter than cheap budget summer tyres in winter, so if you have premium summer tyres, then you could put buying winter tyres on hold until you got better funding, and you just reply on your driver skills during winter.
By the time budget tyres have reached the legal limit, money-wise, it may be a bad time to buy a new set. I would feel like saying "Why now? Couldn't those tyres have worn out next year? I don't have much money
this year!"
It may be worth thinking about going for mid-range or premium tyres, either summer tyres or all-season tyres, and budget winter tyres (assuming if not going for all-season), that way, you would stop worrying about how soon the budge summer tyres is going to last and if you can afford replacements too soon.
Plus if you needed money for the baby, surely your family would like to help chip-in some of the costs? Most grandparents would be happy to help out buying few new clothes for the baby, they would rather help with the baby but not with your car.
If it was me: I would go for premium summer tyres and use them during winter, just as long as I use driver skills to get through safety, and opt to think about buying winter tyres for winter of 2020-21, and hopefully no worries about buying new tyres until around 2025(ish) depending on how many miles I clock up, and if premium tyres haven't yet reached legal limit. That way, for next few years, I spend more on the baby. But that's just me.