what you are proposing is joint physical custody.
there are qualifications for claiming head of household, they are described on the tax papers. if you qualify (and you would with children living there), yes - you can claim it. usually, there is a legal residence for the kids. even in a joint physical situation. the judge will pick where their legal residence is. that parent usually claims the children on the taxes. remember to have it written into the decree who gets to claim them. sometimes it is awarded to the CP, other times it is split and it is an every other year thing. just be sure that it is detailed.
vacation times are usually agreed upon by the parents. if you don't think that he could be agreeable, try adding a clause to the decree that states vacation will be available to either parent for the period of 1 week, at the discretion of the parent. and that there is at least a 2 week or a month notification required. that way, he can't really say no and if he does, it could be contempt.
relocation - is a change of circumstance. you would have to petition the court or have permission of the ex to relocate. there are different requireiments in some states, but most go by the same formulas.
check out
http://www.childcustody.net/page2.htm
that answers alot of questions on custody and relocation. including what the requirements are and the point tests used by the courts.
