If any of the children are under 18, she can. Child support is determined not just on the amount of time spent with each parent, but on a complicated formula which also factors in the income of both parents, so that in some cases, a higher-earning parent may be required to pay child support to the lower-earning parent, although the higher earner also has the child(ren) with him more than 50% of the time.
To figure out your best options, you should review all the facts of your situation...
How is she "restricting" your communication and travel? How is she restricting your relatives from visiting? If you're an adult, you can go where, and when, you please, and if you have the right to occupy a home (whether you are4 a renter or owner) you have the right to invite anyone you want there.
This would be, most appropriately, a "motion to set aside" under CCP 473, due to "inadvertence mistake or excusable neglect". You should prepare the documents and get the motion filed and served as soon as possible; your time limit is a "reasonable time", which cannot be GREATER than six months, but should be as soon as you can get this done.
Notwithstanding the earlier answer (from an attorney outside of California), if you get a "quickie offshore divorce" from a place where you don't really live, and someone decides to make a fuss later, the "quickie offshore divorce" is probably NOT valid, under the California version of the Uniform Divorce Recognition Act.
You may wish to take it to an EXPERIENCED family law attorney to review ALL the facts, but it's probably, absent something really unusual, too late to move to vacate a judgment that's more than two years old, if you participatde in the case at the time..
If you and he sell the house, then if you and he made enough on the sale, there could be taxes due on the gain, which would get divided equally. Since the transfer of title to him, and his payment of money to you, if set up properly, is not a taxable event, none of the money he pays you should be taxable.
It LOOKS like there was a document missing when the documents were submitted in March, and that the missing document was submitted in April. You're not divorced until the judgment is ENTERED, and you, or your lawyer, get the judgment with the judge's signature stamp on it, and a "Notice of Entry of Judgment" back from the court..
Sounds like a complete scam. There's NO reason that I can imagine that you'd need to send a cent before meeting with the attorney, so unless you can INDEPENDENTLY verify that these people are who they say they are, ignore 'em, or better yet, report 'em to the police.