There are too many moving parts, and unknown facts, to your question to give any kind of evaluation of "chances." You do not, for example, specify what the current visitation arrangements are, whether you have any kind of job prospects where you intend to go (although you do mention housing), or what difficulties the other 3 children are having where they are due to the unspecified "whole story."
If your ex will not give consent, you will need court permission for the relocation over his objection. From what you do say, it appears that you have probably met the threshold "good faith reason" test for relocation, and your evaluation of what to do about visitation and support seems pretty reasonable. For a review of the test, and the cases, see the "relocation" materials posted at http://willicklawgroup.com/child-custody-and-visitation/. Especially look over the Schwartz Factors Worksheet.
For any kind of more meaningful review of the issue, you will have to consult with a family law specialist; these cases are extremely fact-specific, and it is usually impossible by e-mail to do any kind of reasonable inquiry into all of the circumstances that are relevant.
Answered on Sep 02nd, 2014 at 10:10 AM