The benefits of a daycare are: 1) accountability, there are multiple people which helps to ensure checks and balances; 2) there are standards of care and certifications which a good center will ensure; 3) socialization and activities...at that age, our center had baby yoga and multiple daily walks. Also, if the nanny is sick you're SOL while a center will have a backup plan in place.

Having done both, I strongly prefer a daycare center. Obviously, you'll do your homework and make sure your children are in quality, reputable care. There are "bad" centers just like there are "bad" nannies.

If your worried about the cost of a nanny look into a nannyshare

We have one and having a nanny is wonderful. No packing up. Baby can sleep in or wake early and if she'd down for s nap when the nanny comes that's ok too. They go for at least a walk a day. All the bottles and laundry and toys get washed every day or almost everyday for toys. And since baby naps well the house main areas get vacuumed and mopped everyday too and it's lovely coming home to a clean house and a happy baby.
We have lots of nannies and kids in the neighborhood so they will play once she's a little older. Right now they work on tummy time and other skills and listen to music and songs.

If you love the existing daycare and they can take baby too, then that's a good option, but having kids in 2 different daycares sounds like a logistical nightmare to me and if you have to uproot DC1 either way (by putting both kids in a new daycare or by getting a nanny), the nanny would be the best choice if you can afford it. The cost really depends on how much you are paying for daycare and what qualities you want in a nanny. Esp given that you may be able to drop down to part time hours, the nanny route could be a big help for a similar (or even reduced) price tag.

The nanny can let your kids have a schedule that is tailored 100% to their needs. She can create outings and activities that are built around their interests and personalities. And the benefit to you of not having to get everyone up and ready and out of the house can be lifechanging. It's so nice to just get up and feed the kids in their pajamas and know that all the supplies and bottles they need are already here and that the nanny will arrive shortly to finish feeding them, clean up and take over. She also helps keep up with their laundry during the week and runs to the grocery store once a week.

OP here- thanks for the responses. I guess it's at least worth interviewing nannies to see what they offer and find out about rates. It's just hard to imagine uprooting my DD from a daycare that she loves so much.

PPs:
You guys had some superb responses to OP's posting.

Yes, finding a RELIABLE person is super important.
But as you know, working so closely w/young children can expose one to infectious germs so all parents who employ personal nannies should secure a back-up option. Or two!

I say since you are paying childcare for two children, an inhome nanny will be cost effective until your oldest starts school.

We went from daycare to a nanny when we had our second kid so I'll give you some pros/cons.

Pros:
My second hardly ever got sick compared to my first. This could have just been a fluke, but being in daycare meant my first was sick a bunch and we didn't have that the second time around.

We only needed PT care (25-30 hours/week) and could not find a daycare that would allow an infant to go PT so hiring a nanny was less expensive in that respect.

Not having to get 2 kids out of the house by a certain time every morning was/is amazingly easier.

My kids have had a pretty great experience being cared for by a nanny. They've had socialization through playgroups, parks, preschool, etc but have also had down time at home when it would not have otherwise been possible.

We have had nannies who take great care of my kids when they're sick so we have missed zero days for sick kids.

Our current nanny is willing to do light housekeeping and it makes our lives WAY easier.

Cons:
With a nanny you are entirely dependent on a single person for childcare. Our first nanny was unreliable and only lasted about 2 months. Scrambling to deal with her being late or missing a day, and then to find someone new, was incredibly stressful.

Now that my kids are older and we've been doing this for the past 5 years it's obviously WAY more expensive than daycare. This has only been the case since my oldest was in school and my youngest became old enough to have more daycare options. But we are feeling pinched by this point.

Start interviewing nannies to help you decide.

I think for what you will be paying out for daycare for two children, it will be very similar than what a nanny will cost you.
Do some research around your area & see what you come up with.

A four-month old in my opinion is much too young to be in a daycare situation. Much too young.
They will not get the one-on-one individualized attention that all infants require.
The ratio is typically 1 Adult per 4 Infants which is not good at all.

Your baby likely will have to wait his turn to be fed, changed + held. He may spend a lot of the day crying it out.
Plus he will be exposed to multiple germs/illnesses, etc.

With an in-home nanny, you won't have to wake up a sleeping child, pack their things up then drop them off at daycare.
They will have the luxury of sleeping in their own beds, eating in their own high chair as well as playing w/ their own toys & home.

For socialization, a nanny can take your child to playgroups, music/dance classes or even to craft activities in your area.
Though truthfully, both your children are a bit young to be worrying about social skills.

Having a nanny offers flexibility if you are stuck at a meeting or stuck in traffic.

Hope this helps!

I may be posting in the wrong place, but I'm trying to decide between an in-home daycare and getting a nanny. My daughter has been in an in-home daycare for about 1.5 years. She is almost 2.5 y/o. I also have a 2 month old and I'm planning to start working again in 2-4 months. My job is flexible, so it's possible that I could get a part time nanny instead of putting them both in daycare full-time. I'm torn and having trouble deciding what to do. My daughters daycare is small, and at capacity, so having them both in daycare might require moving my daughter from a daycare that has been fantastic so far. On the other hand, getting a nanny is more expensive and the kids would get less interaction with other kids. I'm just not sure what makes more sense as both have pros and cons. I'd love to hear some thoughts/experiences. Thanks!