I don’t think this is necessarily something you can just dictate that your employer accepts because you have decided it does not work for you.
I think whether they may be open to negotiation on this aspect of your work largely depends on your contract and work commitments. But I think if you go in with “I can’t do this, so you just need to accept that”, you might not get the response you are hoping for. Most reasonable employers will try to look at ways to make things work for both you and them. But, at the end of the day it depends on what your contract says and the requirements of your job- if it is essential or indeed just strongly preferred, and travel for meetings/work is stated in your job description/contract, then they can insist you go. Or face the consequences of not fulfilling your employment contract.
if they can’t accommodate you, it might not be because they are terrible employers, it might be because they really do need you to do all aspects of the job they employ you to do. In some roles/workplaces, they might be able to accommodate your “no travel” request- either by making it remote meeting or by sending someone else in your place. But, in some cases, that might not be possible- there all all sorts of plausible reasons for that. Perhaps other members of the team don’t have travel requirements in their job description as it’s not needed in their role, so if they don’t want to travel, they can’t be made to. Other members of the team may be unavailable because they are dealing with other essential work and swapping them in to do part of OP’s job may be too disruptive to the wider business. Or, if the client wants to meet face to face and you are the main/only or preferred contact, or have the required knowledge (possibly specialist or client-specific, for example) that is needed, then this may not be possible to put off until you feel able to leave your daughter with a babysitter or childminder.
I think you should request a meeting with your manager to discuss it, present an alternative way of managing this meeting and if you are adamant no travel going forward, you need to discuss if that is possible.