YANBU to want to keep your existing hours, but YABU if you aren't communicating why, especially if your manager has asked you to try and work it out between yourselves first. I have had this happen plenty of times before - both A & B want something, manager says "Have a chat, see if you can work something out between yourselves to suit you both. If you can't come up with something, let me know and I'll make a formal decision based on the business needs."
In your OP it does come across, and I say this in the nicest way, that you just didn't want to change and were being awkward for the sake of it, but as per your further posts, with the extra information it makes sense and gives your needs more weight as it's not just a personal preference or not wanting to faff with changing your appointment, it's also the physical need for a rest day after 2 consecutive work days.
However, you need to communicate this to your colleague. I was recently your colleague in your situation and it's stressfull from that side too but all she seems to be seeing is you being difficult while she is trying to be as open as possible. She has just transferred to a new team, trying to get to grips with that and the new work and now she's being pitted against an existing team member to keep her schedule (and yes the OP has had this schedule, in this team for a few years, but the other colleague could have had this schedule for the same amount of time just in a different team and the job change may not have been her choice but just because she needed to not be in her old team for whatever reason)
I work in a supermarket and was recently offered a new role within my store, it would be a step up and when I went to the interview I did speak to the department manager about the shift pattern as I have to factor in my DD8 and the childcare arrangements I have. My current department manager knows about my shared custody with my ex and that is factored into my hours - so I am only ever rota'd on evening shifts if it is DDs week with her dad for example - and they're really good about keeping up a dialogue about it. The new job I was promised to keep the same shift patterns, just extra hours on certain days so I agreed ... only when I came to sign the change to my contract it turns out they realised it clashed with the other person in the role and they wanted to entirely change my schedule. There's no way I could have just flipped my childcare overnight - especially as I not only had to factor in the paid childcare but also the arrangement I have with her dad - and I was trying to make it work as I really wanted the job, but the other person just would not budge on anything and I ended up telling the manager there was no way I could fit the new schedule change and so I'd have to pass up on the new role. I know they have every right to refuse to change their schedule but they gave no reason so whilst I was telling myself that the other person may have 1001 reasons not to want to change, in my head I was screaming "But why not?" especially when I went into the meeting with them and the department manager and said "Look, I do X, you want me to do Y, that's impossible because of ... but if we could modify it to Z, so Coworker stayed an extra hour on Monday so I could come in late after dropping off DD, then I'd come in an hour early on Friday so they can go home earlier and the hours are the same, then it's doable" and just got a flat "No" off Coworker, which is giving me nothing to work with towards a compromise.
It's one thing to say "Look, I've tried to change my childcare and there just absolutely no way for me to get childcare on Wednesdays at the moment, is there any wiggle room on you having a different day off?" and getting a "No, I don't want to change" vs "No. I know it's hard with childcare issues but I am on a modified timetable because of my disability and there's no way I can do more than two days in a row, so I need Wednesday for my recovery and for my physio."
Whilst you're not obligated to disclose your disability info or the adjustments you need under the Equality Act, would it really be so bad to give her a little bit of information to help with the decision?