christine- I am going to make some suggestions and this is based solely on my research- planning a 24 night trip to Portugal in May- so no first hand experience yet.
You are trying to cover too much ground in too short a trip- you have 10 nights, is that correct? Count your trip in NIGHTs not days.
A 3 night stay means just 2.5 days or less to sightsee- after you've checked out/traveled to/checked in, and oriented yourselves.
You are going north then way south then north again- that's a lot of time spent driving and sitting in a car- pretty much 3 of your days are on the road.
3 Nights in Porto- in your plan probably not arriving til dinner time so really just 2 days now- not really time for a day trip from here- and you do not need or want a car in Porto. Stopping along the way with a car means dealing with parking, hiding your luggage, etc. Both Tomar and Coimbra should be given at least an overnight stay.
I'd drop Porto- it sounds like you have more interest in Lagos- hiking and beach time?
3 nights in Lisbon- your arrival day is a wash- jet lag and with a 7 month old. Don't expect to be at your lodgings til maybe 2:30 pm at best. That leaves just 2 full days and you want to day trip to Sintra- so really just 1 day for Lisbon.
If your flights are booked already and you have a RT Lisbon- then try to arrange your itinerary to visit Lisbon as your last stay- one less hotel change- and no way would I plan to drive to LIS from Algarve on departure day- too many things can go wrong- and the drive is going to take much longer than you think.
Fly into Lisbon- arrive 11:30
To Sintra- 2 nights- nice place to get over jet lag. Visit 1 sight- National Palace? on arrival day, the other sights next day
(Take a cab or book a car/shuttle from airport- about 30-35 euros- door to door service)
Pick up car as you leave Sintra- Drive to Lagos
Lagos 4 nights- enjoy
Drive back to Lisbon- drop car
Lisbon 4 nights- plenty to do here
Depart LIS 6 pm- so you do still have some time this am. You'll need to be at airport by 3- (assuming you are flying to US)
You will need to make sure your rental car is large enough for the 4 of you and all your luggage and baby accessories
I use AutoEurope.com for all European rentals- they are a US based consolidator with excellent service, best rates.
You can book on their website or give them a call toll free- they are extremely knowledgeable and helpful.