When you begin a spell that takes 1 round or longer to cast, you must continue the invocations, gestures, and concentration from 1 round to just before your turn in the next round (at least). If you lose concentration after starting the spell and before it is complete, you lose the spell.
It would be an unusually lenient GM that would say that starting to cast a second spell doesn't count as losing concentration.
compare to:
Casting a Metamagic Spell: Sorcerers and bards must take more time to cast a metamagic spell (one enhanced by a metamagic feat) than a regular spell. If a spell's normal casting time is 1 standard action, casting a metamagic version of the spell is a full-round action for a sorcerer or bard (except for spells modified by the Quicken Spell feat, which take 1 swift action to cast). Note that this isn't the same as a spell with a 1-round casting time. Spells that take a full-round action to cast take effect in the same round that you begin casting, and you are not required to continue the invocations, gestures, and concentration until your next turn.
I'm not seeing anywhere what you're talking about with not being able to act after the shift.
Shift (Su): At 1st level, you can teleport to a nearby space as a swift action as if using dimension door. This movement does not provoke an attack of opportunity. You must be able to see the space that you are moving into. You cannot take other creatures with you when you use this ability (except for familiars). You can move 5 feet for every two wizard levels you possess (minimum 5 feet). You can use this ability a number of times per day equal to 3 + your Intelligence modifier.
are you seeing something that prohibits you from acting after the shift?
Also are there any swift actions I COULD use in a round in which I begin summoning?
Arcane Strike or a quickened spell beforehand.
Dimensional Agility feat would let you use shift before casting. Some GMs might let you use shift (Su) during a summoning spell, though I imagine many wouldn't.