N1M0N1M's journey

I recently received an offer for a hybrid engineering position that requires me to be in the office three days a week. The job is located about five hours away from where I ultimately want to settle down, which is closer to my family. Currently, I work on-site in an engineering role about four hours from my desired city. The offer does include some relocation assistance, which is great, but I’m considering negotiating for a different arrangement. My plan is to propose that for the first year, I relocate to the job's city and work on-site as required. After that first year, I would like to transition to a schedule where I only need to be in the office two days a week. This would allow me to move closer to my family while still fulfilling my job requirements. The reason for this request is quite personal; my parents are aging and facing some medical issues, so being nearer to them is important to me. I believe that a two-day-per-week arrangement is feasible since I interviewed with another company during my job search that offered a similar schedule. I’m reaching out for advice from anyone who has experience negotiating hybrid work arrangements after receiving an offer. What concerns should I be aware of? Should I negotiate the two-day schedule after the first year or ask for the entire arrangement upfront? Is there anything I could offer to make my proposal more appealing? I’m also worried about the risk of jeopardizing the offer by making this request. Any insights would be greatly appreciated.