Might be a bit late now - just seen the date of the OP but in case you are still considering it - I'm from there but no longer live on the island sadly (just got back after a lovely Easter break there, great weather for a change too!)
You can get the SeaCat from Liverpool which takes just under 3 hrs, or the normal ferry from Heysham which takes 4 hrs. The SeaCat won't go in bad weather though, you'd get transferred to the Heysham boat in that case.
Douglas is the main town with most of the accommodation but I prefer the south of the island (Castletown, Port Erin, Port St.Mary). The beach at Port Erin is ideal for children, and is a good base. Your kids would love the Steam Train, also the electric railway which goes from Douglas to the north of the island (Snaefell, Laxey, Ramsey) and the horse trams which go along the length of the prom in Douglas. I second what supa says about the weather on Snaefell though!
Lots of beautiful glens for walks for you all, amazing scenery. Silverdale has a good playground & boating lake, Glen Maye is good for the beach and has a nice waterfall, I also like Glen Helen.
If the weather is bad, there is a good pool in Douglas with slides etc for the kids, a soft play in Castletown, Villa Marina in Douglas also has a soft play place I believe, also check out the wildlife park at Ballaugh and the Manx Cat sanctuary (all favourites of my family!)
And as a poster above said, avoid TT week (2 wks really) in late May/early June, also MGP which is late August.