Awake time schedule to time based schedule

So my daughter’s daycare would like me to get her on their schedule so she has an easier transition. I’ve always done an awake time schedule so she wakes up when she likes, then 2.5 hours later she has a nap, then 3 hours later she has another nap and 4 hours after that it’s bedtime and it’s worked great for her. Well I’ve been bringing her times closer to the clock based schedule and today was the first day of trying to clock schedule as she woke up at the perfect time... to have her nap 2.5 hours later but she only napped for an hour which is what she’ll do at daycare and waiting that extra 30 mins for nap this afternoon was awful... she just cried hysterically while I changed her and then conked right out? Does it get easier after awhile? Has anyone transitioned to a clock based schedule? Her naps now need to be from 8:30-9:30 and 1-3.