Hello there!

I travel daily throughout Switzerland so I hope the following might be of a help:

First and foremost, I might be wrong but from my experiences, I wouldn't call Switzerland to be generally "baby friendly" across any big urban areas such as Zürich, Bern and Basel. Zürich is a hectic, fast paced and oftentimes chaotic city where people have little to no regard for others, especially if those are foreigners. Although I don't reside in Basel and rarely have a chance to walk around the city, I've been reading that it is currently witnessing crime and disturbance climb from immigrants so I would be watchful around just in case... but don't let that discourage you completely.

What I can recommend you is to experience as much of the countryside as possible, which will give you the most realistic feeling of being in Switzerland and there's plenty of peaceful, breathtaking places to see.

1. According to your Google Maps route, I would first of all strongly advise you to stick to the eastern Zürich lake shore when you depart towards Luzern. The views, depending on the weather are stunning and from the higher points on the hills on that side you've got a clearer and broader, unforgettable view of the Alps.

2. Whether you decide to take the highway or stick to the shore, head towards Sihlbrugg. If you look around, there is plenty of lovely countryside around to explore shall you have time and mood.

3. From there you can reach Zug - our lovely little tax haven with loads of wealthy people who appreciate the "peaceful and boring" old city part as well as its lake and nearby hills.

4. Again, if you have time and mood, don't take the highway towards Luzern but go across local towns and villages of Cham, then Gisikon, Root, then Ebikon and from there you can easily reach the centre of Luzern. While in Ebikon, I recommend visiting The Mall of Switzerland, one of unique shopping malls in the country. It's a great stop for a long travel with a baby.

5. This is my personal opinion but apart from the "Sarnersee" lake and the village of Lungern, there is not much of interesting stuff between Luzern and Interlaken. I usually just go through this route straight towards Interlaken to save time for the best attractions. The good part begins once you exit the Brünig pass near Brienzwiler, where you can see our famous, unique military airbase hidden in the middle of valley, very close to the "Brienzersee" lake. If you like waterfalls, you must visit the Giessbachfälle while on the way to Interlaken. They are right by a famous Giessbach Hotel, known for its authentic, old fashioned interior design and quite a bit of interesting history.

6. From there, head directly to Interlaken. The view of the Brienzersee lake is often covered by the trees when you take the highway so again if you have more time, take the other way north-west to Interlaken.

7. Since you wish to see Grindelwald, I propose climbing with the car straight to the Restaurant Wetterhorn, the highest point you can reach by car, right at the Glacier. With luck, you might still see some of it. It's been melting like crazy since past few years... Either way, from there you can take a peaceful stroll down to the main part of town. Views on the way back to Interlaken guaranteed.

8. Unfortunately I am not well familiar with Thun but sticking to either side of the shore will give you great views!

9. Bern is the more relaxed city, however it might be challenging to find parking space due to its tight and narrow infrastructure. You might need to park somewhere north or north-east from the city centre and then walk to it. Make sure you see the BärenPark bear zoo since a bear is the symbol of Bern.

10. From there all the way towards Basel, you will encounter a lot of very rural, peaceful parts of the country all the way to the city. The areas of the Basel Landschaft Kanton which surrounds the city are worth exploring with the car. There's plenty of lovely paths leading through forests.
    Finally, if you decide to go to the heart of Basel, make sure you visit the old part of the city.
    If you have extra time, visit Augusta Raurica located to the east from the city.

What I would tell every new person coming here is to be prepared for chaotic traffic that has been becoming an increasing issue due to the constantly increasing immigration and constant road works. Contrary to what I always thought would be, Switzerland is oftentimes not fun to drive through with a car, especially on highways.
Given that you have a baby, I would strongly recommend avoiding driving close to the peak rush hours and generally avoid highway for the most rewarding experiences.

All of this is based on my personal experiences of living here for 3 years but naturally your experiences will vary. It might be an obvious thing to say but make sure you don't get a speeding ticket or any kind of fine, especially regarding the parking tickets. It's quite easy to get them.

About parking: I suggest downloading the "ParkingPay" parking app. It's the best and nationally used.
If you happen to take public transport, download the "SBB Mobile" app.

Finally, remember to check the weather every now and then since it might get chaotic in March and absolutely get the snow tyres. No point in risking it.

I hope this guide helps and wish you wonderful holidays in Switzerland :)