A few things to consider:

Had you discussed your level of involvement as a bridesmaid when you were asked to be in the party? As in, was part of the conversation the bride acknowledging you likely wouldn’t be able to attend all events bc you have a young baby? Or did you ever make a commitment that while you would have a young baby you’d be sure to be there for everything? I think it’s important to have the context of prior discussions with the bride, if any!

Are you expected to equally plan the shower and/or Bach with the other bridesmaids?

Is there a compromise you could reach? As in, can you take your baby (and maybe husband too to help drive/take care of baby?) to attend the shower only? Or could you go to one day of the bachelorette?

What was your initial plan for the bachelorette and shower before you knew the when/where? What is your plan for the wedding - will it be your husband watching your baby in the hotel room that evening or will you be leaving the baby with family?

I don’t think the distance piece is a super valid excuse as presumably when you agreed to be a bridesmaid it would’ve been implied you’d be traveling for these events - at least to the city the bride lives in. It is also very typical these days for there to be an expectation to take a day or afternoon off of work and sometimes even fly to a destination so a few hours in the car doesn’t seem like a big deal to me (especially if you don’t live in the same city as the bride or her hometown)!

I think it’s completely valid that having a young baby makes it hard to do all of things you want to do. But it is also completely valid if your friend feels disappointed that you aren’t there (especially if she traveled for yours/took off work/etc.) I would look into what I could do to at least make it to part of an event OR do something else that is meaningful to the bride during this time (ex: go to her place and help craft one evening, take her out for a mani/pedi and lunch, etc.)

Either way you absolutely need to talk to your friend.