The phrase "and constraining their ability" is correct and usable in written English.
It can be used when discussing limitations or restrictions placed on someone's capabilities or potential.
Example: "The new regulations are affecting the team's performance by and constraining their ability to innovate."
Alternatives: "limiting their capacity" or "restricting their potential".
Many Democrats had assumed the issue would be a major political help to them, but some Democratic strategists said Republican claims that Mr. Obama had cut $716 billion from the program had at least partly neutralized the Democratic advantage and constrained their ability to emphasize Medicare in their campaign message.
Dentists commented about their provision of care and interactions with family and about the ways in which the state regulatory context shaped and constrained their ability to offer children certain kinds of care.
This violence increases women's vulnerability to HIV and STI both directly, through forced sex, and indirectly by constraining their ability to negotiate sexual contact and the use of condoms.
In addition, non-Indian manufacturers mentioned export subsidies offered by the Indian Government to Indian manufacturers and exporters as constraining their ability to compete.
The majority of providers had limited clinical knowledge of safer conception methods and of their availability, constraining their ability to counsel and support clients in realizing their reproductive rights.
The easy answers are exhausted, and political leaders face a rising tide of anger that is constraining their ability to make more difficult choices.
For if workers see their real wages fall at the same time as the credit crunch is constraining their ability to borrow, consumer demand will suffer.
These days, say the complainers, banks are required to keep more capital on hand than they need to, constraining their ability to loan.
Such time-limited interaction with physicians was seen as constraining their ability to obtain knowledge/support for behavior change.
24 Haitian government agencies also have limited resources (including staff), constraining their ability to provide effective coordination to the sector.
