Have you worked out the train schedules and how they fit into your plan?
I looked at trains from Sintra to Evora. There are very few trains from Lisbon (where you transfer) to Evora. I picked Monday, Sept 12 at random. There are trains from Lisbon at around 7 and 9 am, then at 1.30, 5 and 7 pm. The train website says to transfer at Lisboa-Sete Rios. If you book as a single trip, it's 5-8 minutes transfer time for a total of 2 hours travel time, but the transfer time is only 5-8 minutes. I'm unfamiliar with the station and that may be ample time (with luggage) but I'd be a bit leery of the urban train from Sintra being on time and the IC train from Lisbon waiting for it. So I'd book a slightly earlier train from Sintra and make a separate reservation for IC to Evora. That means either leaving Sintra pretty early (and maybe being in the rush hour crowd to Lisbon), going mid-day and not having enough time in either city, or arriving in Evora in the evening. That would determine how you split the nights between the two.
Depending on what time you arrive in Lisbon from Coimbra, it may be better to take uber or taxi to Sintra. When I visited in 2019, rates were very reasonable and the shortened travel time and ease would be well worth a few extra euros. From the Sintra train station, it's a 10-15 minute walk to the historic center - and it's mostly cobblestones so it may take longer and will likely be uncomfortable walking with wheeled luggage. And if you're going to take a taxi from the train, you might as well take it from Lisbon.
My other observation is that you don't seem to have left much time at all to see Lisbon, with only 3 full days there and 3 half-day trips. I think Coimbra needs one full day, which translates to 2 nights. I'm in the minority, but I was not overly impressed by Evora.