Should we live in Lausanne or Bern?

Wouldn't you want to live near the work so as to cut down the commute, and the commuting costs? The two cities are 60 to 90 minutes apart, with you presumably somewhere in between, so easy enough to get to for activities but a bit far for a daily commute, eh?

Can your daughter go to a local school? Kids pick up languages incredibly quickly.

I would recommend visiting the areas you are interested in and the schools in advance of your move. Even though a school is international, they are all very different. The most desirable usually have waiting lists. If you are considering a public school, you may also want to consider how long you will live here and what your children will need to study in order to transition afterwards. My children are now grown, but with each move we have made, we found the schools we wanted and then found a place to live which would accommodate our commute.

All the up-and-down in Lausanne will get old quickly.

Lausanne has more "life" than Bern - an old adage says that Bern is double as large as the Vienna cemetery but only half as fun. This is somewhat uncharitable as all Swiss city try to get some culture life, always within their generally orderly framework.
I agree with the advice here above, stay by the work place and commute to leisure activities instead of the other way round; you will find cheaper housing and probably better quality of life (very high everywhere in Switzerland) in the country.

You will discover that you German goes little way in Switzerland, as the German speakers prefer a local dialect hard to understand even to real Germans. The Swiss French is more standard. It is not uncommon that in a conversation each party speaks his/her own language, or that sentences begin in a language and end up in another one.

What a lovely problem to have to choose which city in Switzerland to live in! Such a fantastic country! Since you're in Prague already I would suggest hopping a cheapy flight the Switzerland to go look at both cities and, more importantly, the schools. For me, that would be the priority. Maybe the schools are equally good though?
I would not live in Lausanne with it being on a steep, sloping hill that goes up from the lake...if you have personal fitness goals it might be great but if not, it could become awful after a while. Have you looked at the town of Vevey right next door? My cousin and her husband lived there for a number of years (he worked for Nestle) and loved it. We have been there many times as well and it's a beautiful town right along Lake Geneva. I don't know how old your daughter is but it's only a 15 minute train ride between the two towns...if she's old enough she could ride the train to school in Lausanne...if not you would be able to easily take her.
Personally I would live along Lake Geneva rather than Bern. Bern is very nice but I always prefer living near large bodies of water. Bern has a nice river but it's not quite the same.
Your German will not be of much help in Lausanne...they speak primarily French there although I'm sure some will speak a little of the Swiss version of German. The German spoken in Switzerland is a little hard for me to wrap my head around...it's not quite the same as the Hochdeutsch I learned in school. It's Swissdeutsch (or some such name) and I honestly have a hard time understanding them. You'll probably get used to it though after you've been there a while.
Good luck and let us know what you eventually decide!

Have a look at this forum: https://www.englishforum.ch. It's very expensive and probably difficult to find a flat or a house in Lausanne / Lake Geneva.

Thank you all so much for the help! I should have made it clear that of course we will be going to Switzerland a few times on reconnaissance missions--to check out schools, neighborhoods, travel times, housing, etc. But the feedback about the hills in Lausanne is helpful because our daughter has a disability that makes walking uphill difficult for her. So it looks like it'll probably be Bern. Thank you again.

I wanted to mention that although the city of Lausanne has some steep hills, most families live on the outskirts or suburbs of the city as housing is larger, will oftentimes have a yard, and not the multi levels that the city has. There is an excellent international school in Le Mont sur Lausanne and many of the families who have children who attend live in nearby Lutry and Pully, which are both very nice. Although housing can be high and is in demand, it is available and if you are working with a relocation company, you will have no problem finding it. If you are interested in looking at what is available for rent, I have placed links below to help you get an idea. Keep in mind that some relocation companies have families who they know are moving and those listings may not be advertised, but may be available to you.
Homegate.ch
Anibis.ch
I have visited Bern which is very nice but also has many steep hills. Your exploratory trip will help you to decide what suits your family best.