After a little bit of research (mostly involving Wikipedia

), here's my suggestion.
Easiest would be for George Calvert to die of plague in 1630, as almost happened, but that feels like cheating.
Sir John Harvey, serving as governor of Virginia 1630-1635, 1637-1639, favored Lord Baltimore over Claiborne (not sure why, but i suspect money was involved) and, in 1635, removed Claiborne from his position of Secretary of State. This was what prompted Harvey's first impeachment. I'm thinking that if Harvey does something really stupid and gets run out of Virginia in 1634, that would give Claiborne two or three years of support from John West, who replaced Harvey as governor 1635-1636. (I'm assuming that West and Claiborne were friends. In any case, Claiborne had to have some influential friends to get Harvey kicked out for dismissing him.) At the least, Claiborne will still have his position as Secretary of State to bring some more strength to bear in his struggle against Maryland and Thomas Cornwallis, Commissioner of Maryland.
In 1635, Cornwallis seized one of Claiborne's pinnaces. OTL, Claiborne tried to get it back by force and was whupped. ITTL, Virginia puts a little muscle on Claiborne's side and gets his pinnace back. (Peacefully or not, does it really matter? Maybe.) A little fringe effect of this is that legislative power in Maryland is passed from the proprietor to an assembly a year or two sooner than OTLs 1638.
Getting in the home stretch here, according to Wikipedia (I admit to some slight doubts, but i'll go with it anyway) the death knell of Claiborne's initial tenure on Kent Island was when his attorneys, Cloberry and Co., who were concerned about not getting enough money to recoup their investment, took possession of the settlement (how does an attorney take possession of a settlement with it's own small military? Legal possession, i guess) and ordered Claiborne to return to England so they could sue him. Then they invited Maryland to take over by force, which it did.
ITTL, Claiborne has some of the pressure of survival taken off him by having more support from Virginia, and his people can spend more time getting furs, trapping and trading and whatever. His attorneys get enough money to keep them happy and off his back. Calvert can still cause legal trouble for him with the authorities back in England, but i think in, say, 1641, Claiborne gets a patent from the king for his new settlement and preempts any more of that sort of thing. Settlement prior to the grant to Calvert, sufficient strength to keep New Sweden in check, and backing of Virginia (i'm sure that if Harvey got back in, he's out again) are all points in his favor, so i think he's got a good chance.
That's survival settled, now how about some other issues?
OTL, the Susquehannocks were good buddies with New Sweden, trading with them and such and so on. In 1642, Maryland fought a war against them and the Susquehannocks, with the aid of New Sweden, defeated Maryland by 1644. By the time Claiborne was 'evicted' from Kent Island, he had good relations with these same Susquehannocks, trading for beaver furs and such. ITTL, i'm not sure how this would go as Kent Island and New Sweden are both trading with the Susquehannocks and vying for their favor. Further down the road, ill-advised attacks against the Susquehannocks were part of the start of Bacon's Rebellion. I think that will be completely different if the Susquehannocks are Claiborne's allies.
This brings us to Ingle's piracy and invasion of Maryland in 1644. This could be another good PoD as Claiborne assisted Ingle in an attempt to get Kent Island back. He definitely won't help ITTL, no reason to, and might even help Maryland, if asked. But i doubt it.
I've heard that there is a dispute about which branch of the Potomac River the Virginia/Maryland border follows. ITTL, i think the matter may get settled as it being the South Branch, which gives Maryland most of West Virginia's eastern panhandle.
Final thoughts. Remember Claiborne's friend West from the third paragraph? OTL, in 1650 he sold the plantation he'd lived at since 1630 and moved. Where to ITTL? Claiborne's colony, of course, 'cause I say so. His brother was Thomas West, 3rd Baron De La Warr, and the town where his OTL next plantation was was originally called (ya ready for it?) Delaware.
My only problem with this whole thing is that Kent Island could end up as part of Virginia. Maybe if Kent's survival looks set, Maryland would help them so as to weaken Virginia.
A couple of non-Wiki sources:
Exploring Maryland's Roots Library: William Claiborne (1600-c.1677)
Sir John Harvey
Encyclopedia >*John West (governor)