Newmom, I don't think you're considering boundaries prematurely. Your baby will be here before you know it, and you've heard disturbing things about MIL's behavior. Of course, IMO, you should prepare now for what you plan to do - not wait till she endangers your child before you set some limits. TG, DH is on the same page as you and not blind to his mum's faults.
I definitely agree with the no-babysitting idea. Also, I would let her know not to arrive uninvited - and I would not let her in the house if she did. It's wonderful that you respect her feelings, and I think you have given her some very wise and kind replies. However, after this, I would not engage. If she brings up a topic already discussed, I would just say, "We already told you what we're doing about that" or something of that nature and change the subject.
In fact, you don't really need to discuss vaccines, etc. w/ her, at all. IMO, it's ok that she gave you her opinion on these things, but she doesn't have a say in them and doesn't need to be consulted or convinced. There's a saying, "Don't JADE (justify, argue, defend, explain)" your decisions to difficult people. I think it may apply here.
Glad you refused the car seat! Not only can carseats become damaged, etc., but, as you say yourself, safety standards change over the years.
Would it help if DH let her know the boundaries, etc? Some people respond better to their own AC than a DIL or SIL.
Unfortunately, I'm afraid MIL's expectations will be dashed and her feelings are likely to be hurt. But you and DH have to protect your child, your family unit, and your sanity. Sadly, your relationship w/ MIL may change - I hope not, but it might. It's not unusual for parent/AC and MIL/DIL relationships to change when the first baby comes, and sometimes, it's b/c of issues like these.
It's not as if you're cutting her off completely, just limiting her alone-time and preventing her from taking over (arriving unannounced and waking child). She's very lucky, IMO, that she will still be included.