Yes, have done it twice in the last two years by public transport, our kids love it.
Ok, first on transport, there are basically two ways, perhaps there are more from your area, but coming from western switzerland, we have done it this way:
--Basel, Basel BBhof, long trip along German side to Ulm, change in Ulm, to Gunzburg, Legobus from Gunzburg bhof to Legoland
--via Winterthur, Schaffasen, change in Ulm, to Gunzburg, again bus from Gunzburg
Things to keep in mind--1) even though SBB/CFF should be able to sell you the ticket on the German DB, we have never been able to do it, thus bought the ticket for the German side (German DB office) in Basel BBhof. 2) if you have swiss AG or half price fare it makes more sense to cross over on the Schaffausen link, as you pay for less time in Germany on DB. 3) Legoland bus runs very frequently and have always had no problems here; however at one point SBB/DB said to buy ticket with end destination legoland and this bus price was included; another time this was not offered and final destination was Gunzburg. Bus was not 'free' as I recall, but very inexpensive.
As for accomodation, we stayed in legoland village, as the travel hassle with 3 kids was just not worth it. However we had a 4-person house, as youngest still baby and had a crib. There are less expensive housing options in the Lego village, ie. camping car (yours) or the lego tents. However, we went in the Oct. holidays last year and it was very very cold. I could not imagine camping at that time, our little heater was running all the time in the little village house. Often you get an all inclusive package by staying in the village with the park entrance included. Make sure to compare all costs, as for staying outside the park was not significantly cheaper for a lot more hassle. If staying in the village, eat a big breakfast there, price is included with room, and eat light in the park for lunch. To be honest, after swiss prices, everything there seemed to be such a bargain. Everything in park is included in entrance price except perhaps those chance games. Also, legoland 4-person vs. 6 person is the same size house, only 6 person has a loft above main room. The 4 person has main room with double bed and small room with bunk beds. Not sure where to stick a grown 3rd kid, you would probably need the 6-person room. By staying in the legoland village you also get extra perks--lego themed room, minigolf, visit park in evening for special events, get entry in park earlier than other guests, and can walk back anf forth at any time for naps, breaks, etc.