You don't say this but you infer - that your sister is a freeloader and has mooched off of family members for 5 years. And this includes you and your husband - whom she made a play for the last time she and her kids lived with you.
Is your family aware that Sis made a play for your husband the last time she lived with you?
And is your family also aware of the additional costs having 3 extra people in your household - the cable bills, the long distance bills, food bills, transportation, cleaning, etc. cost you the last time you "helped" sis?
And is your family also aware of the drama that Sis brings with her - The kids father, her friends, her kids friends, their belongings, the noise, crowding, tension etc. that you had to deal with for 2 years - the last time you "helped" sis?
If not - then make sure they know this in a calm, but firm, manner. Be pepared to share documents (like phone bills etc. etc.) with the non-believers.
If you feel you have no choice but to help sis one more time, contact your local housing authority and speak with someone who handles subsidised housing. No it's not always in slummy, run down neighborhoods - often subsidised housing can be in modest neighborhoods.
Then write a letter to your sister stating that you and your husband are willing to go out on a limb financially and pay the security deposit and first month's rent on a modest house/apt of her own (on a bus line of course) of up to XXX amount -provided she works with the Housing Authority representative. The rest - utility bills, continued rent, upkeep, food etc. is up to her.