Questions about Portugal Trip

1. No! Rent a car for flexibility and ability to stop when and where you want. 2.. Do not skip Coimbra!
2. Absolutely not! Obidos is good for two hour max. Sadly, it is a town that exists for tourism.Do NOT stay in Obidos. We did and regretted it. Parking was a nightmare. Stop and see Alcobaça on way driving north.
3. No, nor enough time. Take a day cruise up the river, train back to Porto if you have enough time, add a day? Go to Fodors.com and then Wirope, Portugal. Then google Maribel for great insight on Portugal.

First, I would suggest using the train. You won't have to worry about navigating the busy, confusing streets of ancient cities that were built long before anyone was thinking about cars or convenient parking. (One wrong move driving in a busy city like Lisbon or Porto, and your trip could be ruined.) Outside the big urban areas, a car can make for greater flexibility, but you don't seem to have enough travel time in which to be flexible.
I would not recommend skipping Coimbra. True, you have allotted only one night for it (12 June), which will make for a rather rushed view of a city that would normally require two nights. However, the hotel you selected is, I believe, right in the medieval center, and thus close to much of what you will want to see, and I imagine it could be a memorable stay. I haven't been to Obidos, and so can't compare it to Coimbra, but I believe that Obidos could be more "touristy."
With only one complete (non-travel) day in Porto, 14 June, it's hard to imagine squeezing in a Douro Valley trip (or any other side-trip), unless there's nothing whatsoever that you want to see in Porto.

I'd suggest you look at slowing that trip down a bit. It's a whole lot of on-the-move—check in, settle in, pack up, check out, move on... That's busy for a solo traveler, but can be truly laborious for a family of five. You could be challenged to find a balance between seeing a lot and everyone actually enjoying the trip.

Paraphrasing what someone here said recently, "You can only move as quickly as the slowest member of the party, and that could be a different person in each situation"

I too had to cancel my June 2020 trip and will be back in Portugal this summer!! You're going to love Portugal, this will be my third trip there and I can't wait to see all the places on my itinerary. I think your schedule looks great for a first visit. You can always come back some other year and see more and in more detail. I think for what you're planning to do, the train is totally fine. You don't need a rental car, which are very expensive this summer. Two nights in Coimbra is totally fine and will break up the big cities of Lisbon/Porto nicely. If you take a morning train to Coimbra you can totally see the sights in one afternoon. It's not a big town. I would probably spend your two days in Porto in the town. There's lots to see there, and you can do the Duoro Valley the next time. You could do a boat tour in the Porto area if you really want to get on the water.

In Sintra, just stick to the sights there. Cascais is too much to squeeze in and not as interesting, except for the beach. You can easily get out to Cascais when you're in Lisbon if the beach is something you are really interested in. The coast is also very accessible from Porto, though the water will probably be too cold for swimming.

Don't worry, you're doing a great job planning this trip!!

I like your itinerary. We did almost the exact same thing a few years ago, but in 16 days versus the 10 days you have available.
--Going to Sintra direct by car transfer from the airport is perfect! We did exacty that. If you get an early start the following day you will be able to see a couple of popular attractions before the day trippers arrive from Lisbon. I highly recommend that you ask your hotel to recommend a driver/guide to ferry you around by car to Sintra's outlying sites on the one full day you have there. We used the services of Sintra Limo (family owned company) for a full day while there. It was a very pleasant experience and they were very reasonably priced. Vera was our driver from the airport on arrival and her father, Carlos, spent the entire next day getting us to all the popular Sintra attractions in an efficient manner. That was a few years back, so best to ask your hotel for a recommendation and check in advance about pricing. They may be familiar with Sintra Limo (Carlos or Vera).
--I would take the train versus renting a car for the rest of the trip.
--I would skip Obidos, for sure. We stayed there one night, but found it to be very touristy. Our best memories of Obidos are observing the town/setting from afar.
--As to Coimbra, it is a wonderful place to visit, but your schedule only alots one overnight. We prefer at least two overnights wherever we visit so that we have one full (non-travel) day to spend enjoying the stop.
--Soooo, given your time available, i would skip Coimbra on this trip and take the train directly to Porto from Lisbon. If you are in Coimbra for only the one night, it seems like that will not do it justice and you will be rushed. Also, skipping Coimbra gives you one extra night is Porto and there is plenty to do there.

Those are my thoughts, but whatever you decide will be great. Portugal is wonderful!
K

Normally I would agree with the above comment ("Kfrog"); stopping for just one night at a great town may not be worth it, and Coimbra deserves at least two (I think I stayed four); but you may want to make an exception here -- as I mentioned above, your hotel appears to be in the old medieval section, and I'm sure that even one night in a nice hotel, as your selected one seems to be, in an intriguing old historic neighborhood, could be a great experience, especially if you could get into town by early afternoon.
And if you do get in early enough, you could add to the experience, if you're interested, by attending a fado perfomance (Coimbra style) at an intimate venue called Fado ao Centro. The one I attended (2017) was a low-keyed, friendly affair, which ended with the guests mingling with the performers and hostess over glasses of port. (They were university students, so of course they spoke English.) Anyway, if you're interested, you may need reservations for your June visit; they have a web-site. (And of course I don't know how things might have changed, because of Covid or otherwise, since I was there.)

We just returned from the RS Heart of Portugal tour - some thoughts:

1. Obviously, we were on a bus, but - while highways are great, the city streets in all of these towns are VERY narrow, cobblestoned and often used by pedestrians. Parking would be a nightmare (especially in Porto from what we saw).

2 and 3. Skip Obidos, go to Coimbre.

1. The Douro is beautiful, not sure kids would be interested? I agree with previous poster that a boat tour of some sort out of Porto would probably be of more interest to them and get you the views you want.

Other thoughts, with kids in mind:
A) Sintra is great and lots to do and see.
B) Lisbon - recommend the Sao Jorge castle - fun climb to get there, view and park and peacocks are great. Trip out to Belem for cathedral, cloister, tower, and nata (custard tarts). Hop-on/off trolley or bus rides are always a fun way to get a feel for a town. TukTuk tours are also usually great, kids will love it. (Ask questions even if you know what you want, as this will help determine English fluency level. And drivers are often willing to add/sub other stops on their set tours).
C) Coimbre - might be best to find a tour/tour guide here to get the most out of this university town.
D) Porto - Livraria Lello bookstore is pretty cool and inspired the Harry Potter books (go early, get tickets online). Tuk Tuk tours here as well. Cable car on the Gaia side. WOW (World of Wine) is for kids and adults, part of it is about chocolate! We saw school groups there. Taylor's port lodge has a great audio tour and garden, but perhaps not a kid thing? Peacocks and a rooster there for entertainment while adults have port :) Would also recommend a trip out to Afurada (fishing town on Gaia side) for grilled fish (easy but long walk along the river). Beach time if you want it can be an easy bus ride to the "cheese castle" area between Foz and Matusinhos - boardwalk along the beach, surfers, parks, a seaworld-type museum...

Have fun!