Just got hired at a new full time job and keeping my part time job, but there is a conflict in schedules, don't know whether to bring this up to my new job.

My current part time job is the one I've had for 4 years now, management likes me, my coworkers like me, it's the office job I had through university and it paid well as a student. This job is an administrative job with the ministry of health so not like there is a conflict of interest between the 2 jobs. I just graduated nursing school and landed a job as a public health nurse and it pays double what I'm getting at my part time job but it's specific to COVID response and therefore the job is temporary, probably lasting a few months. I think this would be a great opportunity for me and would hate to give it up because of a few scheduling conflicts. It would look great on my resume and would allow me to make a good amount of money for a few months. Whereas my part time job pays way less but has been my stable job I've been able to pay rent off of and live pretty frugally with.

There are a lot of scheduling issues with the new job as they have scheduled me Sunday-Thursday 10am-6pm with Friday and Saturday off, and my part time job is usually Tuesday & Friday 4-8pm with alternating weekends. I've been able to speak to some coworkers and get them to cover me on some days and weekends but there is one reoccuring weekly shift the Tuesday 4-8 at my part time job that I'm not able to get covered, and I can't just show up 3 hours late to my shift, so asking my current manager to compromise isn't even an option I think.

So I'm thinking my only option is to speak to the new manager and ask them if I can be changed to the 8-4 shift just on Tuesdays so I can rush to my 2nd job. In the job offer they stated my schedule was fixed and that I had to work all the offers but I'm wondering if there may be some flexibility to that. I'm afraid I might come off as being uncooperative or difficult having just been a new hire and I'm scared of jeopardizing my contract with them or having them let me go. They hired 15 other nurses as well.

I'm getting mixed advice from different people. Some people are telling me it's best to be honest from the get go and let the new job know about my scheduling issues and that I've tried my best to resolve them with my other job but am having difficulty with this one day every week and that this would be easier to figure out from the start rather than wait till after orientation and bring it up 2 weeks after starting. And some people are telling me this could come off as me not being dedicated to this new job and that I'm being difficult and would leave a bad impression to the point they would let me go, or that it looks bad that I', working a party time job ontop of this. Quitting my part time job is not an option as I need this after my contract ends with my new one. I really need some advice about what to say to the new job and when I should say it, or if it's even a good idea to say anything. I didn't indicate there might be a scheduling issue with my interview with HR on the phone because I was afraid they would pass me up if I let on there may be scheduling issues. I start tomorrow. Thank you in advance!

TL; DR: Just got a new second job with scheduling conflicts with my current part time job, wondering how to approach new job about changing the timing of 1 weekly shift despite already been given a fixed schedule.

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