When our children got older and began to scatter across the country, we decided to rent it out weekly as a vacation condo since we weren't using it as much.

You did not mention anything about having a spouse or any children and my answers assume you do not have any. 

Our overall goals are to have a bunch of free time to be able to travel, and also start building up wealth for our 4 children.

He is a widower and has his own two sons in college, so I wouldn't want to use his money for my children's college educationI have some unclear financial matters with this rental plan and need some advice.1.

He is no longer on the lease and the children are young.

My advice to my daughter and son-in-law as they did not want multi-family, either, and wanted to buy a home to live in,  not just investment property, was to buy something that needs some work, plan to fix it up within the 2-year tax-credit time period, sell and keep profits tax-free, then buy another one that needs work and repeat until children need a solid school district.   

I have acquired a rare illness which means that I have become disabled over the past year, with small children.

Further the adult children may with to move out on their own during the lease period.

-mother of two small children- my schedule is not the most flexible (being full-time working mother of two with husband in medical school) but I have carved out some time over this summer that would lend itself to my real estate endeavorsWho you are:-experienced real estate investor (rentals, flips, etc.)

-Exactly 3 weeks after telling me how it wasn't their fault and they weren't damaging the place on purpose, one of the unsupervised children used a lighter and started a fire under a bed in the master bedroom.