As a father that has traveled to many countries with my child, I can tell you which one will be worse...The night bus! The reason being is this; waking your children up at 4.30am and having to do "the walk of doom" across the border (2 sets of immigration and customs with your luggage) your children won't be happy. You may have to carry your 3 year old part of the way, and with your luggage that won't be fun. Also both your children have been traveling for about 24 hours at that point, so they'll be tired.
By going to Chetumal you are breaking the trip up in two parts which will be easier on everybody. There are hotel rooms in Chetumal for around $25usd, and they are reasonably nice, so it's not a huge expense. R/t taxi should not be more then $15usd. Id still go to Playa, have some fun at the beach, and try to catch a bus around 5pm to Chetumal. You should get in to Chetumal around 10pm (that's an estimate, not sure exact time of that trip). That may be a little ambitious though, so you might just want to go direct to Chetumal, get there around 7pm...grab a nice dinner (they have good restaurants there), find a hotel, and watch some random Spanish TV at your hotel room before you crash out...get a good nights rest and up bright and early for a beautiful boat ride to San Pedro.