First babies are often overdue. As PP says, a 4.5 hour car journey at less than 2 weeks postpartum is likely to be extremely uncomfortable and potentially risky (thrombosis) for your partner as well as for baby, particularly if she has a c-section - the seatbelt goes right over where the incision is. Babies of that age also need to feed frequently, often every couple of hours during the day and if your partner is breastfeeding she will probably still be getting to grips with it, which usually means that doing it in public is awkward and stressful, let alone a series of uncomfortable motorway service stations which might also not feel that clean. Feeding can also take a very long time while mum & baby are learning what to do. And some babies are refluxy and need to be held upright for ~30 mins after feeding or they vomit everywhere. Neither of you are likely to be sleeping very well. If there are any complications with either mum or baby, you might still be in hospital.
Could the visit be postponed or family come to you?
Anyway if you want more opinions on that you will probably find them if you post that specific question in Parenting, Pregnancy, Travel, Chat, or AIBU.
For the car seat question - the only true lie flat ones, negating time limits, are carrycots. None of those seats are a carrycot, and carrycots have disadvantages in the car (less crash safety and take up more space, don't last as long.)
The i-Level is the one of the three which lies flattest, but it's not a carrycot (not sure why the listing says you don't need a carrycot - it's not suitable for overnight sleep).
It does lie flatter than a standard car seat but there aren't any studies saying how long is reasonable in a seat like that, so the standard guidance still applies. It is approximately a 23 degree incline, plus whatever the incline of your rear car seats is (usually somewhere between 5-15 degrees). The Fisher Price Rock n Play, which was recalled in the US a couple of years ago due to causing deaths, was a 30 degree incline. Advice is that safe sleep is less than a 10 degree incline.
Out of the three seats personally I would go for the Aton B2. It has a good base with adjustable isofix to counteract an inclined seat, it's easy to use, will last a decent amount of time and it's not overpriced.
But I'd rethink the drive if possible. First few weeks you want to stay close to home.