Updated Answer
My original answer used chicago, because it's a highly developed style which I thought came close to what was wanted. However, a comment in response indicated that the questioner has developed his/her own custom .bbx style based on authortitle-ibid, and I think there are likely to be conflicts there.
Frankly, I don't think authortitle-ibid is the place to start: a key feature of the style you want is (a) full citations at first and (b) short citations on subsequent use. The standard style that comes close to this is verbose-ibid, and that is probably the right place to start. It's still more likely to be compatible with your custom adjustments, since it won't be far from authortitle-ibid as far as full citations is concerned, and it will certainly be closer than chicago. If you start from authortitle you are going to have to recreate all the structure for full citations and so forth that is already present in verbose, which is pointless.
Within the verbose-ibid style, the typesetting of shortened citations is handled by the bibmacro cite:short, and so we redefine that.
\documentclass{article}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@book{author1,
author = {Author, A.},
title = {First Work},
date = {2010},
publisher = {Publisher},
}
@book{author2,
author = {Author, A.},
title = {Second Work},
date = {2010},
publisher = {Publisher},
}
@book{author3,
author = {Author, A.},
title = {Third Work},
date = {2011},
publisher = {Publisher},
}
\end{filecontents}
\setlength{\textheight}{2in}
\usepackage[style=verbose-ibid,labeldate=true]{biblatex}
\makeatletter
\renewbibmacro*{cite:short}{%
\printnames{labelname}%
\iffieldundef{extrayear}%
{\setunit*{\addspace}%
\printtext[bibhyperlink]{%
\mkbibparens{\printdatelabel}}}
{\setunit*{\nametitledelim}%
\printtext[bibhyperlink]{%
\printfield[citetitle]{labeltitle}%
\setunit*{\addspace}%
\printtext{\mkbibparens{\printdatelabel}}}}}
\makeatother
\addbibresource{\jobname.bib}
\addbibresource{biblatex-examples.bib}
\begin{document}
We use \texttt{verbose-ibid} as our style, setting \texttt{labeldate}
true so as to have a hook to decide if we have multiple works by the
same author(s) in the same year.
We revise the \texttt{cite:short} macro. On the first occasion
something is printed, we will have full citations.\footcite{author1,
author2, author3} On subsequent occasions they will be shortened,
with titles added only if necessary for
disambiguation.\footcite{author1, author2, author3}
\end{document}
Producing:

Original Answer
The effect you want is nearly the default with the biblatex-chicago style, with the notes option: it is loaded (unusually) as a free-standing package not a style, but it makes full use of biblatex. The documentation is extensive.
Indeed, I first thought that this just did what you want: but I was reading too quickly -- the default is to have an author/title style on subsequent citations, not the mixture of author/year and title you suggest. That can, however, be fairly easily accomplished by redefining one bibmacro: we also need to add the labeldate option, not because we add any additional labels this way, but because it's a handy way of getting biber to tell us if there is more than one relevant citation in a given year. The basic technique could, I think, be easily adapted to the standard styles.
A brief example follows:
\documentclass{article}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@book{author1,
author = {Author, A.},
title = {First Work},
date = {2010},
}
@book{author2,
author = {Author, A.},
title = {Second Work},
date = {2010},
}
@book{author3,
author = {Author, A.},
title = {Third Work},
date = {2011},
}
\end{filecontents}
\usepackage[notes,labeldate=true]{biblatex-chicago}
\makeatletter
\renewbibmacro*{cite:short}{%
\ifthenelse{\ifnameundef{labelname}\OR%
\ifentrytype{inreference}\OR%
\ifentrytype{reference}\OR%
\ifentrytype{mvreference}}%
{\iffieldequalstr{entrysubtype}{magazine}% Simplify .bib creation
{\ifuseauthor%
{\printfield[journaltitle]{journaltitle}\isdot\newcunit}%
{}}%
{\ifentrytype{manual}%
{\printlist{organization}\isdot\newcunit}%
{}}}%
{\iffieldequalstr{authortype}{anon}%
{\bibleftbracket\printnames{labelname}%
\bibrightbracket\classicpunct}%
{\iffieldequalstr{authortype}{anon?}%
{\bibleftbracket\printnames{labelname}?%
\bibrightbracket\classicpunct}%
{\usebibmacro{choose+labelname}%\printnames{labelname}%
\isdot\classicpunct}}}%
\iffieldundef{extrayear}% Is the reference unique?
{\setunit*{\addspace}}% No: change punctuation from comma to space ready for year
{\printfield[citetitle]{labeltitle}% Yes: print the title
\setunit*{\addspace}}%
\ifboolexpr{%
togl {cms@allshort}%
or
test {\ifbibliography}
}%
{\printtext[bibhyperref]{%
\mkbibparens{\printdatelabel}}}% We want the date label not the title
{\printtext[cmshyperlink]{%
\mkbibparens{\printdatelabel}}}% We want the date label not the title
}%:\thefield{entrytype}?
\makeatother
\addbibresource{\jobname.bib}
\addbibresource{biblatex-examples.bib}
\begin{document}
With \texttt{biblatex-chicago} with the \texttt{notes} option, the
default is for citation to appear in footnotes, with a full citation
on the first occasion and an abbreviated citation on subsequent occasions.
So the first citation is full,\footcite{author1} an immediately
following citation will use \emph{ibid}\footcite[Thus:][]{author1},
(unless \texttt{ibidtracker} is set false) but otherwise later
citations will be abbreviated.
We do, however, have to make minor modifications to one macro, because
by default the package assumes author/title citations, but we have to
provide author/year citations, with the date printed only if there is
more than one work in the relevant year. We thus get all our full
citations out,\footcite{author1, author2, author3} and then
demonstrate that happening.\footcite{author1, author2, author3}
\end{document}

authortitlestyle with anauthordatestyle? Normally, when the year alone doesn't disambiguate, you add a letter. Smith 2001a vs Smith 2001b vs Smith 2002 --- no one is going to be confused as to which is which. When you use titles, you disambiguate via theshorttitlefield, which is what gets printed in subsequent citations. – jon May 16 '14 at 14:19shorttilefield? – jon May 16 '14 at 14:29.bibentry (thus mimicking normal authortitle conventions like Chicago); but the requirements you were given do not qualify as normal... – jon May 16 '14 at 14:37